test_transform.py

##
#   Copyright 2019-2021 Contributors
#
#   Licensed under the Apache License, Version 2.0 (the "License");
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
#
#       http://www.apache.org/licenses/LICENSE-2.0
#
#   Unless required by applicable law or agreed to in writing, software
#   distributed under the License is distributed on an "AS IS" BASIS,
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and
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from scipy import sparse as spsp
import networkx as nx
import numpy as np
import os
import dgl
import dgl.function as fn
import dgl.partition
import backend as F
import unittest
import math
import pytest
from test_utils.graph_cases import get_cases
from test_utils import parametrize_idtype

from test_heterograph import create_test_heterograph3, create_test_heterograph4, create_test_heterograph5

D = 5

# line graph related

def test_line_graph1():
    N = 5
    G = dgl.DGLGraph(nx.star_graph(N)).to(F.ctx())
    G.edata['h'] = F.randn((2 * N, D))
    L = G.line_graph(shared=True)
    assert L.number_of_nodes() == 2 * N
    assert F.allclose(L.ndata['h'], G.edata['h'])
    assert G.device == F.ctx()

@parametrize_idtype
def test_line_graph2(idtype):
    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1, 1, 2, 2],[2, 0, 2, 0, 1])
    }, idtype=idtype)
    lg = dgl.line_graph(g)
    assert lg.number_of_nodes() == 5
    assert lg.number_of_edges() == 8
    row, col = lg.edges()
    assert np.array_equal(F.asnumpy(row),
                          np.array([0, 0, 1, 2, 2, 3, 4, 4]))
    assert np.array_equal(F.asnumpy(col),
                          np.array([3, 4, 0, 3, 4, 0, 1, 2]))

    lg = dgl.line_graph(g, backtracking=False)
    assert lg.number_of_nodes() == 5
    assert lg.number_of_edges() == 4
    row, col = lg.edges()
    assert np.array_equal(F.asnumpy(row),
                          np.array([0, 1, 2, 4]))
    assert np.array_equal(F.asnumpy(col),
                          np.array([4, 0, 3, 1]))
    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1, 1, 2, 2],[2, 0, 2, 0, 1])
    }, idtype=idtype).formats('csr')
    lg = dgl.line_graph(g)
    assert lg.number_of_nodes() == 5
    assert lg.number_of_edges() == 8
    row, col = lg.edges()
    assert np.array_equal(F.asnumpy(row),
                          np.array([0, 0, 1, 2, 2, 3, 4, 4]))
    assert np.array_equal(F.asnumpy(col),
                          np.array([3, 4, 0, 3, 4, 0, 1, 2]))

    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1, 1, 2, 2],[2, 0, 2, 0, 1])
    }, idtype=idtype).formats('csc')
    lg = dgl.line_graph(g)
    assert lg.number_of_nodes() == 5
    assert lg.number_of_edges() == 8
    row, col, eid = lg.edges('all')
    row = F.asnumpy(row)
    col = F.asnumpy(col)
    eid = F.asnumpy(eid).astype(int)
    order = np.argsort(eid)
    assert np.array_equal(row[order],
                          np.array([0, 0, 1, 2, 2, 3, 4, 4]))
    assert np.array_equal(col[order],
                          np.array([3, 4, 0, 3, 4, 0, 1, 2]))

def test_no_backtracking():
    N = 5
    G = dgl.DGLGraph(nx.star_graph(N))
    L = G.line_graph(backtracking=False)
    assert L.number_of_nodes() == 2 * N
    for i in range(1, N):
        e1 = G.edge_id(0, i)
        e2 = G.edge_id(i, 0)
        assert not L.has_edge_between(e1, e2)
        assert not L.has_edge_between(e2, e1)

# reverse graph related
@parametrize_idtype
def test_reverse(idtype):
    g = dgl.DGLGraph()
    g = g.astype(idtype).to(F.ctx())
    g.add_nodes(5)
    # The graph need not to be completely connected.
    g.add_edges([0, 1, 2], [1, 2, 1])
    g.ndata['h'] = F.tensor([[0.], [1.], [2.], [3.], [4.]])
    g.edata['h'] = F.tensor([[5.], [6.], [7.]])
    rg = g.reverse()

    assert g.is_multigraph == rg.is_multigraph

    assert g.number_of_nodes() == rg.number_of_nodes()
    assert g.number_of_edges() == rg.number_of_edges()
    assert F.allclose(F.astype(rg.has_edges_between(
        [1, 2, 1], [0, 1, 2]), F.float32), F.ones((3,)))
    assert g.edge_id(0, 1) == rg.edge_id(1, 0)
    assert g.edge_id(1, 2) == rg.edge_id(2, 1)
    assert g.edge_id(2, 1) == rg.edge_id(1, 2)

    # test dgl.reverse
    # test homogeneous graph
    g = dgl.graph((F.tensor([0, 1, 2]), F.tensor([1, 2, 0])))
    g.ndata['h'] = F.tensor([[0.], [1.], [2.]])
    g.edata['h'] = F.tensor([[3.], [4.], [5.]])
    g_r = dgl.reverse(g)
    assert g.number_of_nodes() == g_r.number_of_nodes()
    assert g.number_of_edges() == g_r.number_of_edges()
    u_g, v_g, eids_g = g.all_edges(form='all')
    u_rg, v_rg, eids_rg = g_r.all_edges(form='all')
    assert F.array_equal(u_g, v_rg)
    assert F.array_equal(v_g, u_rg)
    assert F.array_equal(eids_g, eids_rg)
    assert F.array_equal(g.ndata['h'], g_r.ndata['h'])
    assert len(g_r.edata) == 0

    # without share ndata
    g_r = dgl.reverse(g, copy_ndata=False)
    assert g.number_of_nodes() == g_r.number_of_nodes()
    assert g.number_of_edges() == g_r.number_of_edges()
    assert len(g_r.ndata) == 0
    assert len(g_r.edata) == 0

    # with share ndata and edata
    g_r = dgl.reverse(g, copy_ndata=True, copy_edata=True)
    assert g.number_of_nodes() == g_r.number_of_nodes()
    assert g.number_of_edges() == g_r.number_of_edges()
    assert F.array_equal(g.ndata['h'], g_r.ndata['h'])
    assert F.array_equal(g.edata['h'], g_r.edata['h'])

    # add new node feature to g_r
    g_r.ndata['hh'] = F.tensor([0, 1, 2])
    assert ('hh' in g.ndata) is False
    assert ('hh' in g_r.ndata) is True

    # add new edge feature to g_r
    g_r.edata['hh'] = F.tensor([0, 1, 2])
    assert ('hh' in g.edata) is False
    assert ('hh' in g_r.edata) is True

    # test heterogeneous graph
    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1, 2, 4, 3 ,1, 3], [1, 2, 3, 2, 0, 0, 1]),
        ('user', 'plays', 'game'): ([0, 0, 2, 3, 3, 4, 1], [1, 0, 1, 0, 1, 0, 0]),
        ('developer', 'develops', 'game'): ([0, 1, 1, 2], [0, 0, 1, 1])},
        idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h'] = F.tensor([0, 1, 2, 3, 4])
    g.nodes['user'].data['hh'] = F.tensor([1, 1, 1, 1, 1])
    g.nodes['game'].data['h'] = F.tensor([0, 1])
    g.edges['follows'].data['h'] = F.tensor([0, 1, 2, 4, 3 ,1, 3])
    g.edges['follows'].data['hh'] = F.tensor([1, 2, 3, 2, 0, 0, 1])
    g_r = dgl.reverse(g)

    for etype_g, etype_gr in zip(g.canonical_etypes, g_r.canonical_etypes):
        assert etype_g[0] == etype_gr[2]
        assert etype_g[1] == etype_gr[1]
        assert etype_g[2] == etype_gr[0]
        assert g.number_of_edges(etype_g) == g_r.number_of_edges(etype_gr)
    for ntype in g.ntypes:
        assert g.number_of_nodes(ntype) == g_r.number_of_nodes(ntype)
    assert F.array_equal(g.nodes['user'].data['h'], g_r.nodes['user'].data['h'])
    assert F.array_equal(g.nodes['user'].data['hh'], g_r.nodes['user'].data['hh'])
    assert F.array_equal(g.nodes['game'].data['h'], g_r.nodes['game'].data['h'])
    assert len(g_r.edges['follows'].data) == 0
    u_g, v_g, eids_g = g.all_edges(form='all', etype=('user', 'follows', 'user'))
    u_rg, v_rg, eids_rg = g_r.all_edges(form='all', etype=('user', 'follows', 'user'))
    assert F.array_equal(u_g, v_rg)
    assert F.array_equal(v_g, u_rg)
    assert F.array_equal(eids_g, eids_rg)
    u_g, v_g, eids_g = g.all_edges(form='all', etype=('user', 'plays', 'game'))
    u_rg, v_rg, eids_rg = g_r.all_edges(form='all', etype=('game', 'plays', 'user'))
    assert F.array_equal(u_g, v_rg)
    assert F.array_equal(v_g, u_rg)
    assert F.array_equal(eids_g, eids_rg)
    u_g, v_g, eids_g = g.all_edges(form='all', etype=('developer', 'develops', 'game'))
    u_rg, v_rg, eids_rg = g_r.all_edges(form='all', etype=('game', 'develops', 'developer'))
    assert F.array_equal(u_g, v_rg)
    assert F.array_equal(v_g, u_rg)
    assert F.array_equal(eids_g, eids_rg)

    # withour share ndata
    g_r = dgl.reverse(g, copy_ndata=False)
    for etype_g, etype_gr in zip(g.canonical_etypes, g_r.canonical_etypes):
        assert etype_g[0] == etype_gr[2]
        assert etype_g[1] == etype_gr[1]
        assert etype_g[2] == etype_gr[0]
        assert g.number_of_edges(etype_g) == g_r.number_of_edges(etype_gr)
    for ntype in g.ntypes:
        assert g.number_of_nodes(ntype) == g_r.number_of_nodes(ntype)
    assert len(g_r.nodes['user'].data) == 0
    assert len(g_r.nodes['game'].data) == 0

    g_r = dgl.reverse(g, copy_ndata=True, copy_edata=True)
    print(g_r)
    for etype_g, etype_gr in zip(g.canonical_etypes, g_r.canonical_etypes):
        assert etype_g[0] == etype_gr[2]
        assert etype_g[1] == etype_gr[1]
        assert etype_g[2] == etype_gr[0]
        assert g.number_of_edges(etype_g) == g_r.number_of_edges(etype_gr)
    assert F.array_equal(g.edges['follows'].data['h'], g_r.edges['follows'].data['h'])
    assert F.array_equal(g.edges['follows'].data['hh'], g_r.edges['follows'].data['hh'])

    # add new node feature to g_r
    g_r.nodes['user'].data['hhh'] = F.tensor([0, 1, 2, 3, 4])
    assert ('hhh' in g.nodes['user'].data) is False
    assert ('hhh' in g_r.nodes['user'].data) is True

    # add new edge feature to g_r
    g_r.edges['follows'].data['hhh'] = F.tensor([1, 2, 3, 2, 0, 0, 1])
    assert ('hhh' in g.edges['follows'].data) is False
    assert ('hhh' in g_r.edges['follows'].data) is True


@parametrize_idtype
def test_reverse_shared_frames(idtype):
    g = dgl.DGLGraph()
    g = g.astype(idtype).to(F.ctx())
    g.add_nodes(3)
    g.add_edges([0, 1, 2], [1, 2, 1])
    g.ndata['h'] = F.tensor([[0.], [1.], [2.]])
    g.edata['h'] = F.tensor([[3.], [4.], [5.]])

    rg = g.reverse(share_ndata=True, share_edata=True)
    assert F.allclose(g.ndata['h'], rg.ndata['h'])
    assert F.allclose(g.edata['h'], rg.edata['h'])
    assert F.allclose(g.edges[[0, 2], [1, 1]].data['h'],
                      rg.edges[[1, 1], [0, 2]].data['h'])

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_to_bidirected():
    # homogeneous graph
    elist = [(0, 0), (0, 1), (1, 0),
             (1, 1), (2, 1), (2, 2)]
    num_edges = 7
    g = dgl.graph(tuple(zip(*elist)))
    elist.append((1, 2))
    elist = set(elist)
    big = dgl.to_bidirected(g)
    assert big.number_of_edges() == num_edges
    src, dst = big.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == set(elist)

    # heterogeneous graph
    elist1 = [(0, 0), (0, 1), (1, 0),
                (1, 1), (2, 1), (2, 2)]
    elist2 = [(0, 0), (0, 1)]
    g = dgl.heterograph({
        ('user', 'wins', 'user'): tuple(zip(*elist1)),
        ('user', 'follows', 'user'): tuple(zip(*elist2))
    })
    g.nodes['user'].data['h'] = F.ones((3, 1))
    elist1.append((1, 2))
    elist1 = set(elist1)
    elist2.append((1, 0))
    elist2 = set(elist2)
    big = dgl.to_bidirected(g)
    assert big.number_of_edges('wins') == 7
    assert big.number_of_edges('follows') == 3
    src, dst = big.edges(etype='wins')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == set(elist1)
    src, dst = big.edges(etype='follows')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == set(elist2)

    big = dgl.to_bidirected(g, copy_ndata=True)
    assert F.array_equal(g.nodes['user'].data['h'], big.nodes['user'].data['h'])

def test_add_reverse_edges():
    # homogeneous graph
    g = dgl.graph((F.tensor([0, 1, 3, 1]), F.tensor([1, 2, 0, 2])))
    g.ndata['h'] = F.tensor([[0.], [1.], [2.], [1.]])
    g.edata['h'] = F.tensor([[3.], [4.], [5.], [6.]])
    bg = dgl.add_reverse_edges(g, copy_ndata=True, copy_edata=True)
    u, v = g.edges()
    ub, vb = bg.edges()
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    assert F.array_equal(g.ndata['h'], bg.ndata['h'])
    assert F.array_equal(F.cat([g.edata['h'], g.edata['h']], dim=0), bg.edata['h'])
    bg.ndata['hh'] = F.tensor([[0.], [1.], [2.], [1.]])
    assert ('hh' in g.ndata) is False
    bg.edata['hh'] = F.tensor([[0.], [1.], [2.], [1.], [0.], [1.], [2.], [1.]])
    assert ('hh' in g.edata) is False

    # donot share ndata and edata
    bg = dgl.add_reverse_edges(g, copy_ndata=False, copy_edata=False)
    ub, vb = bg.edges()
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    assert ('h' in bg.ndata) is False
    assert ('h' in bg.edata) is False

    # zero edge graph
    g = dgl.graph(([], []))
    bg = dgl.add_reverse_edges(g, copy_ndata=True, copy_edata=True, exclude_self=False)

    # heterogeneous graph
    g = dgl.heterograph({
        ('user', 'wins', 'user'): (F.tensor([0, 2, 0, 2, 2]), F.tensor([1, 1, 2, 1, 0])),
        ('user', 'plays', 'game'): (F.tensor([1, 2, 1]), F.tensor([2, 1, 1])),
        ('user', 'follows', 'user'): (F.tensor([1, 2, 1]), F.tensor([0, 0, 0]))
    })
    g.nodes['game'].data['hv'] = F.ones((3, 1))
    g.nodes['user'].data['hv'] = F.ones((3, 1))
    g.edges['wins'].data['h'] = F.tensor([0, 1, 2, 3, 4])
    bg = dgl.add_reverse_edges(g, copy_ndata=True, copy_edata=True, ignore_bipartite=True)
    assert F.array_equal(g.nodes['game'].data['hv'], bg.nodes['game'].data['hv'])
    assert F.array_equal(g.nodes['user'].data['hv'], bg.nodes['user'].data['hv'])
    u, v = g.all_edges(order='eid', etype=('user', 'wins', 'user'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'wins', 'user'))
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    assert F.array_equal(F.cat([g.edges['wins'].data['h'], g.edges['wins'].data['h']], dim=0),
                         bg.edges['wins'].data['h'])
    u, v = g.all_edges(order='eid', etype=('user', 'follows', 'user'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'follows', 'user'))
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    u, v = g.all_edges(order='eid', etype=('user', 'plays', 'game'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'plays', 'game'))
    assert F.array_equal(u, ub)
    assert F.array_equal(v, vb)
    assert set(bg.edges['plays'].data.keys()) == {dgl.EID}
    assert set(bg.edges['follows'].data.keys()) == {dgl.EID}

    # donot share ndata and edata
    bg = dgl.add_reverse_edges(g, copy_ndata=False, copy_edata=False, ignore_bipartite=True)
    assert len(bg.edges['wins'].data) == 0
    assert len(bg.edges['plays'].data) == 0
    assert len(bg.edges['follows'].data) == 0
    assert len(bg.nodes['game'].data) == 0
    assert len(bg.nodes['user'].data) == 0
    u, v = g.all_edges(order='eid', etype=('user', 'wins', 'user'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'wins', 'user'))
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    u, v = g.all_edges(order='eid', etype=('user', 'follows', 'user'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'follows', 'user'))
    assert F.array_equal(F.cat([u, v], dim=0), ub)
    assert F.array_equal(F.cat([v, u], dim=0), vb)
    u, v = g.all_edges(order='eid', etype=('user', 'plays', 'game'))
    ub, vb = bg.all_edges(order='eid', etype=('user', 'plays', 'game'))
    assert F.array_equal(u, ub)
    assert F.array_equal(v, vb)

    # test the case when some nodes have zero degree
    # homogeneous graph
    g = dgl.graph((F.tensor([0, 1, 3, 1]), F.tensor([1, 2, 0, 2])), num_nodes=6)
    g.ndata['h'] = F.tensor([[0.], [1.], [2.], [1.], [1.], [1.]])
    g.edata['h'] = F.tensor([[3.], [4.], [5.], [6.]])
    bg = dgl.add_reverse_edges(g, copy_ndata=True, copy_edata=True)
    assert g.number_of_nodes() == bg.number_of_nodes()
    assert F.array_equal(g.ndata['h'], bg.ndata['h'])
    assert F.array_equal(F.cat([g.edata['h'], g.edata['h']], dim=0), bg.edata['h'])

    # heterogeneous graph
    g = dgl.heterograph({
        ('user', 'wins', 'user'): (F.tensor([0, 2, 0, 2, 2]), F.tensor([1, 1, 2, 1, 0])),
        ('user', 'plays', 'game'): (F.tensor([1, 2, 1]), F.tensor([2, 1, 1])),
        ('user', 'follows', 'user'): (F.tensor([1, 2, 1]), F.tensor([0, 0, 0]))},
        num_nodes_dict={
            'user': 5,
            'game': 3
        })
    g.nodes['game'].data['hv'] = F.ones((3, 1))
    g.nodes['user'].data['hv'] = F.ones((5, 1))
    g.edges['wins'].data['h'] = F.tensor([0, 1, 2, 3, 4])
    bg = dgl.add_reverse_edges(g, copy_ndata=True, copy_edata=True, ignore_bipartite=True)
    assert g.number_of_nodes('user') == bg.number_of_nodes('user')
    assert g.number_of_nodes('game') == bg.number_of_nodes('game')
    assert F.array_equal(g.nodes['game'].data['hv'], bg.nodes['game'].data['hv'])
    assert F.array_equal(g.nodes['user'].data['hv'], bg.nodes['user'].data['hv'])
    assert F.array_equal(F.cat([g.edges['wins'].data['h'], g.edges['wins'].data['h']], dim=0),
                         bg.edges['wins'].data['h'])

    # test exclude_self
    g = dgl.heterograph({
        ('A', 'r1', 'A'): (F.tensor([0, 0, 1, 1]), F.tensor([0, 1, 1, 2])),
        ('A', 'r2', 'A'): (F.tensor([0, 1]), F.tensor([1, 2]))
    })
    g.edges['r1'].data['h'] = F.tensor([0, 1, 2, 3])
    rg = dgl.add_reverse_edges(g, copy_edata=True, exclude_self=True)
    assert rg.num_edges('r1') == 6
    assert rg.num_edges('r2') == 4
    assert F.array_equal(rg.edges['r1'].data['h'], F.tensor([0, 1, 2, 3, 1, 3]))

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_simple_graph():
    elist = [(0, 1), (0, 2), (1, 2), (0, 1)]
    g = dgl.DGLGraph(elist, readonly=True)
    assert g.is_multigraph
    sg = dgl.to_simple_graph(g)
    assert not sg.is_multigraph
    assert sg.number_of_edges() == 3
    src, dst = sg.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == set(elist)

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def _test_bidirected_graph():
    def _test(in_readonly, out_readonly):
        elist = [(0, 0), (0, 1), (1, 0),
                (1, 1), (2, 1), (2, 2)]
        num_edges = 7
        g = dgl.DGLGraph(elist, readonly=in_readonly)
        elist.append((1, 2))
        elist = set(elist)
        big = dgl.to_bidirected_stale(g, out_readonly)
        assert big.number_of_edges() == num_edges
        src, dst = big.edges()
        eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
        assert eset == set(elist)

    _test(True, True)
    _test(True, False)
    _test(False, True)
    _test(False, False)


@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_khop_graph():
    N = 20
    feat = F.randn((N, 5))

    def _test(g):
        for k in range(4):
            g_k = dgl.khop_graph(g, k)
            # use original graph to do message passing for k times.
            g.ndata['h'] = feat
            for _ in range(k):
                g.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
            h_0 = g.ndata.pop('h')
            # use k-hop graph to do message passing for one time.
            g_k.ndata['h'] = feat
            g_k.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
            h_1 = g_k.ndata.pop('h')
            assert F.allclose(h_0, h_1, rtol=1e-3, atol=1e-3)

    # Test for random undirected graphs
    g = dgl.DGLGraph(nx.erdos_renyi_graph(N, 0.3))
    _test(g)
    # Test for random directed graphs
    g = dgl.DGLGraph(nx.erdos_renyi_graph(N, 0.3, directed=True))
    _test(g)

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_khop_adj():
    N = 20
    feat = F.randn((N, 5))
    g = dgl.DGLGraph(nx.erdos_renyi_graph(N, 0.3))
    for k in range(3):
        adj = F.tensor(F.swapaxes(dgl.khop_adj(g, k), 0, 1))
        # use original graph to do message passing for k times.
        g.ndata['h'] = feat
        for _ in range(k):
            g.update_all(fn.copy_u('h', 'm'), fn.sum('m', 'h'))
        h_0 = g.ndata.pop('h')
        # use k-hop adj to do message passing for one time.
        h_1 = F.matmul(adj, feat)
        assert F.allclose(h_0, h_1, rtol=1e-3, atol=1e-3)


@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_laplacian_lambda_max():
    N = 20
    eps = 1e-6
    # test DGLGraph
    g = dgl.DGLGraph(nx.erdos_renyi_graph(N, 0.3))
    l_max = dgl.laplacian_lambda_max(g)
    assert (l_max[0] < 2 + eps)
    # test batched DGLGraph
    '''
    N_arr = [20, 30, 10, 12]
    bg = dgl.batch([
        dgl.DGLGraph(nx.erdos_renyi_graph(N, 0.3))
        for N in N_arr
    ])
    l_max_arr = dgl.laplacian_lambda_max(bg)
    assert len(l_max_arr) == len(N_arr)
    for l_max in l_max_arr:
        assert l_max < 2 + eps
    '''

def create_large_graph(num_nodes, idtype=F.int64):
    row = np.random.choice(num_nodes, num_nodes * 10)
    col = np.random.choice(num_nodes, num_nodes * 10)
    spm = spsp.coo_matrix((np.ones(len(row)), (row, col)))
    spm.sum_duplicates()

    return dgl.from_scipy(spm, idtype=idtype)

def get_nodeflow(g, node_ids, num_layers):
    batch_size = len(node_ids)
    expand_factor = g.number_of_nodes()
    sampler = dgl.contrib.sampling.NeighborSampler(g, batch_size,
            expand_factor=expand_factor, num_hops=num_layers,
            seed_nodes=node_ids)
    return next(iter(sampler))

# Disabled since everything will be on heterogeneous graphs
@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
def test_partition_with_halo():
    g = create_large_graph(1000)
    node_part = np.random.choice(4, g.number_of_nodes())
    subgs, _, _ = dgl.transforms.partition_graph_with_halo(g, node_part, 2, reshuffle=True)
    for part_id, subg in subgs.items():
        node_ids = np.nonzero(node_part == part_id)[0]
        lnode_ids = np.nonzero(F.asnumpy(subg.ndata['inner_node']))[0]
        orig_nids = F.asnumpy(subg.ndata['orig_id'])[lnode_ids]
        assert np.all(np.sort(orig_nids) == node_ids)
        assert np.all(F.asnumpy(subg.in_degrees(lnode_ids)) == F.asnumpy(g.in_degrees(orig_nids)))
        assert np.all(F.asnumpy(subg.out_degrees(lnode_ids)) == F.asnumpy(g.out_degrees(orig_nids)))

@unittest.skipIf(os.name == 'nt', reason='Do not support windows yet')
@unittest.skipIf(F._default_context_str == 'gpu', reason="METIS doesn't support GPU")
@parametrize_idtype
def test_metis_partition(idtype):
    # TODO(zhengda) Metis fails to partition a small graph.
    g = create_large_graph(1000, idtype=idtype)
    if idtype == F.int64:
        check_metis_partition(g, 0)
        check_metis_partition(g, 1)
        check_metis_partition(g, 2)
        check_metis_partition_with_constraint(g)
    else:
        assert_fail = False
        try:
            check_metis_partition(g, 1)
        except:
            assert_fail = True
        assert assert_fail

def check_metis_partition_with_constraint(g):
    ntypes = np.zeros((g.number_of_nodes(),), dtype=np.int32)
    ntypes[0:int(g.number_of_nodes()/4)] = 1
    ntypes[int(g.number_of_nodes()*3/4):] = 2
    subgs = dgl.transforms.metis_partition(g, 4, extra_cached_hops=1, balance_ntypes=ntypes)
    if subgs is not None:
        for i in subgs:
            subg = subgs[i]
            parent_nids = F.asnumpy(subg.ndata[dgl.NID])
            sub_ntypes = ntypes[parent_nids]
            print('type0:', np.sum(sub_ntypes == 0))
            print('type1:', np.sum(sub_ntypes == 1))
            print('type2:', np.sum(sub_ntypes == 2))
    subgs = dgl.transforms.metis_partition(g, 4, extra_cached_hops=1,
                                          balance_ntypes=ntypes, balance_edges=True)
    if subgs is not None:
        for i in subgs:
            subg = subgs[i]
            parent_nids = F.asnumpy(subg.ndata[dgl.NID])
            sub_ntypes = ntypes[parent_nids]
            print('type0:', np.sum(sub_ntypes == 0))
            print('type1:', np.sum(sub_ntypes == 1))
            print('type2:', np.sum(sub_ntypes == 2))

def check_metis_partition(g, extra_hops):
    subgs = dgl.transforms.metis_partition(g, 4, extra_cached_hops=extra_hops)
    num_inner_nodes = 0
    num_inner_edges = 0
    if subgs is not None:
        for part_id, subg in subgs.items():
            lnode_ids = np.nonzero(F.asnumpy(subg.ndata['inner_node']))[0]
            ledge_ids = np.nonzero(F.asnumpy(subg.edata['inner_edge']))[0]
            num_inner_nodes += len(lnode_ids)
            num_inner_edges += len(ledge_ids)
            assert np.sum(F.asnumpy(subg.ndata['part_id']) == part_id) == len(lnode_ids)
        assert num_inner_nodes == g.number_of_nodes()
        print(g.number_of_edges() - num_inner_edges)

    if extra_hops == 0:
        return

    # partitions with node reshuffling
    subgs = dgl.transforms.metis_partition(g, 4, extra_cached_hops=extra_hops, reshuffle=True)
    num_inner_nodes = 0
    num_inner_edges = 0
    edge_cnts = np.zeros((g.number_of_edges(),))
    if subgs is not None:
        for part_id, subg in subgs.items():
            lnode_ids = np.nonzero(F.asnumpy(subg.ndata['inner_node']))[0]
            ledge_ids = np.nonzero(F.asnumpy(subg.edata['inner_edge']))[0]
            num_inner_nodes += len(lnode_ids)
            num_inner_edges += len(ledge_ids)
            assert np.sum(F.asnumpy(subg.ndata['part_id']) == part_id) == len(lnode_ids)
            nids = F.asnumpy(subg.ndata[dgl.NID])

            # ensure the local node Ids are contiguous.
            parent_ids = F.asnumpy(subg.ndata[dgl.NID])
            parent_ids = parent_ids[:len(lnode_ids)]
            assert np.all(parent_ids == np.arange(parent_ids[0], parent_ids[-1] + 1))

            # count the local edges.
            parent_ids = F.asnumpy(subg.edata[dgl.EID])[ledge_ids]
            edge_cnts[parent_ids] += 1

            orig_ids = subg.ndata['orig_id']
            inner_node = F.asnumpy(subg.ndata['inner_node'])
            for nid in range(subg.number_of_nodes()):
                neighs = subg.predecessors(nid)
                old_neighs1 = F.gather_row(orig_ids, neighs)
                old_nid = F.asnumpy(orig_ids[nid])
                old_neighs2 = g.predecessors(old_nid)
                # If this is an inner node, it should have the full neighborhood.
                if inner_node[nid]:
                    assert np.all(np.sort(F.asnumpy(old_neighs1)) == np.sort(F.asnumpy(old_neighs2)))
        # Normally, local edges are only counted once.
        assert np.all(edge_cnts == 1)

        assert num_inner_nodes == g.number_of_nodes()
        print(g.number_of_edges() - num_inner_edges)

@unittest.skipIf(F._default_context_str == 'gpu', reason="It doesn't support GPU")
def test_reorder_nodes():
    g = create_large_graph(1000)
    new_nids = np.random.permutation(g.number_of_nodes())
    # TODO(zhengda) we need to test both CSR and COO.
    new_g = dgl.partition.reorder_nodes(g, new_nids)
    new_in_deg = new_g.in_degrees()
    new_out_deg = new_g.out_degrees()
    in_deg = g.in_degrees()
    out_deg = g.out_degrees()
    new_in_deg1 = F.scatter_row(in_deg, F.tensor(new_nids), in_deg)
    new_out_deg1 = F.scatter_row(out_deg, F.tensor(new_nids), out_deg)
    assert np.all(F.asnumpy(new_in_deg == new_in_deg1))
    assert np.all(F.asnumpy(new_out_deg == new_out_deg1))
    orig_ids = F.asnumpy(new_g.ndata['orig_id'])
    for nid in range(g.number_of_nodes()):
        neighs = F.asnumpy(g.successors(nid))
        new_neighs1 = new_nids[neighs]
        new_nid = new_nids[nid]
        new_neighs2 = new_g.successors(new_nid)
        assert np.all(np.sort(new_neighs1) == np.sort(F.asnumpy(new_neighs2)))

    for nid in range(new_g.number_of_nodes()):
        neighs = F.asnumpy(new_g.successors(nid))
        old_neighs1 = orig_ids[neighs]
        old_nid = orig_ids[nid]
        old_neighs2 = g.successors(old_nid)
        assert np.all(np.sort(old_neighs1) == np.sort(F.asnumpy(old_neighs2)))

        neighs = F.asnumpy(new_g.predecessors(nid))
        old_neighs1 = orig_ids[neighs]
        old_nid = orig_ids[nid]
        old_neighs2 = g.predecessors(old_nid)
        assert np.all(np.sort(old_neighs1) == np.sort(F.asnumpy(old_neighs2)))

@parametrize_idtype
def test_compact(idtype):
    g1 = dgl.heterograph({
        ('user', 'follow', 'user'): ([1, 3], [3, 5]),
        ('user', 'plays', 'game'): ([2, 3, 2], [4, 4, 5]),
        ('game', 'wished-by', 'user'): ([6, 5], [7, 7])},
        {'user': 20, 'game': 10}, idtype=idtype, device=F.ctx())

    g2 = dgl.heterograph({
        ('game', 'clicked-by', 'user'): ([3], [1]),
        ('user', 'likes', 'user'): ([1, 8], [8, 9])},
        {'user': 20, 'game': 10}, idtype=idtype, device=F.ctx())

    g3 = dgl.heterograph({('user', '_E', 'user'): ((0, 1), (1, 2))},
                         {'user': 10}, idtype=idtype, device=F.ctx())
    g4 = dgl.heterograph({('user', '_E', 'user'): ((1, 3), (3, 5))},
                         {'user': 10}, idtype=idtype, device=F.ctx())

    def _check(g, new_g, induced_nodes):
        assert g.ntypes == new_g.ntypes
        assert g.canonical_etypes == new_g.canonical_etypes

        for ntype in g.ntypes:
            assert -1 not in induced_nodes[ntype]

        for etype in g.canonical_etypes:
            g_src, g_dst = g.all_edges(order='eid', etype=etype)
            g_src = F.asnumpy(g_src)
            g_dst = F.asnumpy(g_dst)
            new_g_src, new_g_dst = new_g.all_edges(order='eid', etype=etype)
            new_g_src_mapped = induced_nodes[etype[0]][F.asnumpy(new_g_src)]
            new_g_dst_mapped = induced_nodes[etype[2]][F.asnumpy(new_g_dst)]
            assert (g_src == new_g_src_mapped).all()
            assert (g_dst == new_g_dst_mapped).all()

    # Test default
    new_g1 = dgl.compact_graphs(g1)
    induced_nodes = {ntype: new_g1.nodes[ntype].data[dgl.NID] for ntype in new_g1.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}
    assert new_g1.idtype == idtype
    assert set(induced_nodes['user']) == set([1, 3, 5, 2, 7])
    assert set(induced_nodes['game']) == set([4, 5, 6])
    _check(g1, new_g1, induced_nodes)

    # Test with always_preserve given a dict
    new_g1 = dgl.compact_graphs(
        g1, always_preserve={'game': F.tensor([4, 7], idtype)})
    assert new_g1.idtype == idtype
    induced_nodes = {ntype: new_g1.nodes[ntype].data[dgl.NID] for ntype in new_g1.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}
    assert set(induced_nodes['user']) == set([1, 3, 5, 2, 7])
    assert set(induced_nodes['game']) == set([4, 5, 6, 7])
    _check(g1, new_g1, induced_nodes)

    # Test with always_preserve given a tensor
    new_g3 = dgl.compact_graphs(
        g3, always_preserve=F.tensor([1, 7], idtype))
    induced_nodes = {ntype: new_g3.nodes[ntype].data[dgl.NID] for ntype in new_g3.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}

    assert new_g3.idtype == idtype
    assert set(induced_nodes['user']) == set([0, 1, 2, 7])
    _check(g3, new_g3, induced_nodes)

    # Test multiple graphs
    new_g1, new_g2 = dgl.compact_graphs([g1, g2])
    induced_nodes = {ntype: new_g1.nodes[ntype].data[dgl.NID] for ntype in new_g1.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}
    assert new_g1.idtype == idtype
    assert new_g2.idtype == idtype
    assert set(induced_nodes['user']) == set([1, 3, 5, 2, 7, 8, 9])
    assert set(induced_nodes['game']) == set([3, 4, 5, 6])
    _check(g1, new_g1, induced_nodes)
    _check(g2, new_g2, induced_nodes)

    # Test multiple graphs with always_preserve given a dict
    new_g1, new_g2 = dgl.compact_graphs(
        [g1, g2], always_preserve={'game': F.tensor([4, 7], dtype=idtype)})
    induced_nodes = {ntype: new_g1.nodes[ntype].data[dgl.NID] for ntype in new_g1.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}
    assert new_g1.idtype == idtype
    assert new_g2.idtype == idtype
    assert set(induced_nodes['user']) == set([1, 3, 5, 2, 7, 8, 9])
    assert set(induced_nodes['game']) == set([3, 4, 5, 6, 7])
    _check(g1, new_g1, induced_nodes)
    _check(g2, new_g2, induced_nodes)

    # Test multiple graphs with always_preserve given a tensor
    new_g3, new_g4 = dgl.compact_graphs(
        [g3, g4], always_preserve=F.tensor([1, 7], dtype=idtype))
    induced_nodes = {ntype: new_g3.nodes[ntype].data[dgl.NID] for ntype in new_g3.ntypes}
    induced_nodes = {k: F.asnumpy(v) for k, v in induced_nodes.items()}

    assert new_g3.idtype == idtype
    assert new_g4.idtype == idtype

    assert set(induced_nodes['user']) == set([0, 1, 2, 3, 5, 7])
    _check(g3, new_g3, induced_nodes)
    _check(g4, new_g4, induced_nodes)

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU to simple not implemented")
@parametrize_idtype
def test_to_simple(idtype):
    # homogeneous graph
    g = dgl.graph((F.tensor([0, 1, 2, 1]), F.tensor([1, 2, 0, 2])))
    g.ndata['h'] = F.tensor([[0.], [1.], [2.]])
    g.edata['h'] = F.tensor([[3.], [4.], [5.], [6.]])
    sg, wb = dgl.to_simple(g, writeback_mapping=True)
    u, v = g.all_edges(form='uv', order='eid')
    u = F.asnumpy(u).tolist()
    v = F.asnumpy(v).tolist()
    uv = list(zip(u, v))
    eid_map = F.asnumpy(wb)

    su, sv = sg.all_edges(form='uv', order='eid')
    su = F.asnumpy(su).tolist()
    sv = F.asnumpy(sv).tolist()
    suv = list(zip(su, sv))
    sc = F.asnumpy(sg.edata['count'])
    assert set(uv) == set(suv)
    for i, e in enumerate(suv):
        assert sc[i] == sum(e == _e for _e in uv)
    for i, e in enumerate(uv):
        assert eid_map[i] == suv.index(e)
    # shared ndata
    assert F.array_equal(sg.ndata['h'], g.ndata['h'])
    assert 'h' not in sg.edata
    # new ndata to sg
    sg.ndata['hh'] = F.tensor([[0.], [1.], [2.]])
    assert 'hh' not in g.ndata

    sg = dgl.to_simple(g, writeback_mapping=False, copy_ndata=False)
    assert 'h' not in sg.ndata
    assert 'h' not in sg.edata

    # test coalesce edge feature
    sg = dgl.to_simple(g, copy_edata=True, aggregator='arbitrary')
    assert F.allclose(sg.edata['h'][1], F.tensor([4.]))
    sg = dgl.to_simple(g, copy_edata=True, aggregator='sum')
    assert F.allclose(sg.edata['h'][1], F.tensor([10.]))
    sg = dgl.to_simple(g, copy_edata=True, aggregator='mean')
    assert F.allclose(sg.edata['h'][1], F.tensor([5.]))

    # heterogeneous graph
    g = dgl.heterograph({
        ('user', 'follow', 'user'): ([0, 1, 2, 1, 1, 1],
                                     [1, 3, 2, 3, 4, 4]),
        ('user', 'plays', 'game'): ([3, 2, 1, 1, 3, 2, 2], [5, 3, 4, 4, 5, 3, 3])},
        idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h'] = F.tensor([0, 1, 2, 3, 4])
    g.nodes['user'].data['hh'] = F.tensor([0, 1, 2, 3, 4])
    g.edges['follow'].data['h'] = F.tensor([0, 1, 2, 3, 4, 5])
    sg, wb = dgl.to_simple(g, return_counts='weights', writeback_mapping=True, copy_edata=True)
    g.nodes['game'].data['h'] = F.tensor([0, 1, 2, 3, 4, 5])

    for etype in g.canonical_etypes:
        u, v = g.all_edges(form='uv', order='eid', etype=etype)
        u = F.asnumpy(u).tolist()
        v = F.asnumpy(v).tolist()
        uv = list(zip(u, v))
        eid_map = F.asnumpy(wb[etype])

        su, sv = sg.all_edges(form='uv', order='eid', etype=etype)
        su = F.asnumpy(su).tolist()
        sv = F.asnumpy(sv).tolist()
        suv = list(zip(su, sv))
        sw = F.asnumpy(sg.edges[etype].data['weights'])

        assert set(uv) == set(suv)
        for i, e in enumerate(suv):
            assert sw[i] == sum(e == _e for _e in uv)
        for i, e in enumerate(uv):
            assert eid_map[i] == suv.index(e)
    # shared ndata
    assert F.array_equal(sg.nodes['user'].data['h'], g.nodes['user'].data['h'])
    assert F.array_equal(sg.nodes['user'].data['hh'], g.nodes['user'].data['hh'])
    assert 'h' not in sg.nodes['game'].data
    # new ndata to sg
    sg.nodes['user'].data['hhh'] = F.tensor([0, 1, 2, 3, 4])
    assert 'hhh' not in g.nodes['user'].data
    # share edata
    feat_idx = F.asnumpy(wb[('user', 'follow', 'user')])
    _, indices = np.unique(feat_idx, return_index=True)
    assert np.array_equal(F.asnumpy(sg.edges['follow'].data['h']),
                          F.asnumpy(g.edges['follow'].data['h'])[indices])

    sg = dgl.to_simple(g, writeback_mapping=False, copy_ndata=False)
    for ntype in g.ntypes:
        assert g.number_of_nodes(ntype) == sg.number_of_nodes(ntype)
    assert 'h' not in sg.nodes['user'].data
    assert 'hh' not in sg.nodes['user'].data

    # verify DGLGraph.edge_ids() after dgl.to_simple()
    # in case ids are not initialized in underlying coo2csr()
    u = F.tensor([0, 1, 2])
    v = F.tensor([1, 2, 3])
    eids = F.tensor([0, 1, 2])
    g = dgl.graph((u, v))
    assert F.array_equal(g.edge_ids(u, v), eids)
    sg = dgl.to_simple(g)
    assert F.array_equal(sg.edge_ids(u, v), eids)

@parametrize_idtype
def test_to_block(idtype):
    def check(g, bg, ntype, etype, dst_nodes, include_dst_in_src=True):
        if dst_nodes is not None:
            assert F.array_equal(bg.dstnodes[ntype].data[dgl.NID], dst_nodes)
        n_dst_nodes = bg.number_of_nodes('DST/' + ntype)
        if include_dst_in_src:
            assert F.array_equal(
                bg.srcnodes[ntype].data[dgl.NID][:n_dst_nodes],
                bg.dstnodes[ntype].data[dgl.NID])

        g = g[etype]
        bg = bg[etype]
        induced_src = bg.srcdata[dgl.NID]
        induced_dst = bg.dstdata[dgl.NID]
        induced_eid = bg.edata[dgl.EID]

        bg_src, bg_dst = bg.all_edges(order='eid')
        src_ans, dst_ans = g.all_edges(order='eid')

        induced_src_bg = F.gather_row(induced_src, bg_src)
        induced_dst_bg = F.gather_row(induced_dst, bg_dst)
        induced_src_ans = F.gather_row(src_ans, induced_eid)
        induced_dst_ans = F.gather_row(dst_ans, induced_eid)

        assert F.array_equal(induced_src_bg, induced_src_ans)
        assert F.array_equal(induced_dst_bg, induced_dst_ans)

    def checkall(g, bg, dst_nodes, include_dst_in_src=True):
        for etype in g.etypes:
            ntype = g.to_canonical_etype(etype)[2]
            if dst_nodes is not None and ntype in dst_nodes:
                check(g, bg, ntype, etype, dst_nodes[ntype], include_dst_in_src)
            else:
                check(g, bg, ntype, etype, None, include_dst_in_src)

    g = dgl.heterograph({
        ('A', 'AA', 'A'): ([0, 2, 1, 3], [1, 3, 2, 4]),
        ('A', 'AB', 'B'): ([0, 1, 3, 1], [1, 3, 5, 6]),
        ('B', 'BA', 'A'): ([2, 3], [3, 2])}, idtype=idtype, device=F.ctx())
    g.nodes['A'].data['x'] = F.randn((5, 10))
    g.nodes['B'].data['x'] = F.randn((7, 5))
    g.edges['AA'].data['x'] = F.randn((4, 3))
    g.edges['AB'].data['x'] = F.randn((4, 3))
    g.edges['BA'].data['x'] = F.randn((2, 3))
    g_a = g['AA']

    def check_features(g, bg):
        for ntype in bg.srctypes:
            for key in g.nodes[ntype].data:
                assert F.array_equal(
                    bg.srcnodes[ntype].data[key],
                    F.gather_row(g.nodes[ntype].data[key], bg.srcnodes[ntype].data[dgl.NID]))
        for ntype in bg.dsttypes:
            for key in g.nodes[ntype].data:
                assert F.array_equal(
                    bg.dstnodes[ntype].data[key],
                    F.gather_row(g.nodes[ntype].data[key], bg.dstnodes[ntype].data[dgl.NID]))
        for etype in bg.canonical_etypes:
            for key in g.edges[etype].data:
                assert F.array_equal(
                    bg.edges[etype].data[key],
                    F.gather_row(g.edges[etype].data[key], bg.edges[etype].data[dgl.EID]))

    bg = dgl.to_block(g_a)
    check(g_a, bg, 'A', 'AA', None)
    check_features(g_a, bg)
    assert bg.number_of_src_nodes() == 5
    assert bg.number_of_dst_nodes() == 4

    bg = dgl.to_block(g_a, include_dst_in_src=False)
    check(g_a, bg, 'A', 'AA', None, False)
    check_features(g_a, bg)
    assert bg.number_of_src_nodes() == 4
    assert bg.number_of_dst_nodes() == 4

    dst_nodes = F.tensor([4, 3, 2, 1], dtype=idtype)
    bg = dgl.to_block(g_a, dst_nodes)
    check(g_a, bg, 'A', 'AA', dst_nodes)
    check_features(g_a, bg)

    g_ab = g['AB']

    bg = dgl.to_block(g_ab)
    assert bg.idtype == idtype
    assert bg.number_of_nodes('SRC/B') == 4
    assert F.array_equal(bg.srcnodes['B'].data[dgl.NID], bg.dstnodes['B'].data[dgl.NID])
    assert bg.number_of_nodes('DST/A') == 0
    checkall(g_ab, bg, None)
    check_features(g_ab, bg)

    dst_nodes = {'B': F.tensor([5, 6, 3, 1], dtype=idtype)}
    bg = dgl.to_block(g, dst_nodes)
    assert bg.number_of_nodes('SRC/B') == 4
    assert F.array_equal(bg.srcnodes['B'].data[dgl.NID], bg.dstnodes['B'].data[dgl.NID])
    assert bg.number_of_nodes('DST/A') == 0
    checkall(g, bg, dst_nodes)
    check_features(g, bg)

    dst_nodes = {'A': F.tensor([4, 3, 2, 1], dtype=idtype), 'B': F.tensor([3, 5, 6, 1], dtype=idtype)}
    bg = dgl.to_block(g, dst_nodes=dst_nodes)
    checkall(g, bg, dst_nodes)
    check_features(g, bg)

    # test specifying lhs_nodes with include_dst_in_src
    src_nodes = {}
    for ntype in dst_nodes.keys():
        # use the previous run to get the list of source nodes
        src_nodes[ntype] = bg.srcnodes[ntype].data[dgl.NID]
    bg = dgl.to_block(g, dst_nodes=dst_nodes, src_nodes=src_nodes)
    checkall(g, bg, dst_nodes)
    check_features(g, bg)

    # test without include_dst_in_src
    dst_nodes = {'A': F.tensor([4, 3, 2, 1], dtype=idtype), 'B': F.tensor([3, 5, 6, 1], dtype=idtype)}
    bg = dgl.to_block(g, dst_nodes=dst_nodes, include_dst_in_src=False)
    checkall(g, bg, dst_nodes, False)
    check_features(g, bg)

    # test specifying lhs_nodes without include_dst_in_src
    src_nodes = {}
    for ntype in dst_nodes.keys():
        # use the previous run to get the list of source nodes
        src_nodes[ntype] = bg.srcnodes[ntype].data[dgl.NID]
    bg = dgl.to_block(g, dst_nodes=dst_nodes, include_dst_in_src=False,
        src_nodes=src_nodes)
    checkall(g, bg, dst_nodes, False)
    check_features(g, bg)


@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not implemented")
@parametrize_idtype
def test_remove_edges(idtype):
    def check(g1, etype, g, edges_removed):
        src, dst, eid = g.edges(etype=etype, form='all')
        src1, dst1 = g1.edges(etype=etype, order='eid')
        if etype is not None:
            eid1 = g1.edges[etype].data[dgl.EID]
        else:
            eid1 = g1.edata[dgl.EID]
        src1 = F.asnumpy(src1)
        dst1 = F.asnumpy(dst1)
        eid1 = F.asnumpy(eid1)
        src = F.asnumpy(src)
        dst = F.asnumpy(dst)
        eid = F.asnumpy(eid)
        sde_set = set(zip(src, dst, eid))

        for s, d, e in zip(src1, dst1, eid1):
            assert (s, d, e) in sde_set
        assert not np.isin(edges_removed, eid1).any()
        assert g1.idtype == g.idtype

    for fmt in ['coo', 'csr', 'csc']:
        for edges_to_remove in [[2], [2, 2], [3, 2], [1, 3, 1, 2]]:
            g = dgl.graph(([0, 2, 1, 3], [1, 3, 2, 4]), idtype=idtype).formats(fmt)
            g1 = dgl.remove_edges(g, F.tensor(edges_to_remove, idtype))
            check(g1, None, g, edges_to_remove)

            g = dgl.from_scipy(
                spsp.csr_matrix(([1, 1, 1, 1], ([0, 2, 1, 3], [1, 3, 2, 4])), shape=(5, 5)),
                idtype=idtype).formats(fmt)
            g1 = dgl.remove_edges(g, F.tensor(edges_to_remove, idtype))
            check(g1, None, g, edges_to_remove)

    g = dgl.heterograph({
        ('A', 'AA', 'A'): ([0, 2, 1, 3], [1, 3, 2, 4]),
        ('A', 'AB', 'B'): ([0, 1, 3, 1], [1, 3, 5, 6]),
        ('B', 'BA', 'A'): ([2, 3], [3, 2])}, idtype=idtype)
    g2 = dgl.remove_edges(g, {'AA': F.tensor([2], idtype), 'AB': F.tensor([3], idtype), 'BA': F.tensor([1], idtype)})
    check(g2, 'AA', g, [2])
    check(g2, 'AB', g, [3])
    check(g2, 'BA', g, [1])

    g3 = dgl.remove_edges(g, {'AA': F.tensor([], idtype), 'AB': F.tensor([3], idtype), 'BA': F.tensor([1], idtype)})
    check(g3, 'AA', g, [])
    check(g3, 'AB', g, [3])
    check(g3, 'BA', g, [1])

    g4 = dgl.remove_edges(g, {'AB': F.tensor([3, 1, 2, 0], idtype)})
    check(g4, 'AA', g, [])
    check(g4, 'AB', g, [3, 1, 2, 0])
    check(g4, 'BA', g, [])

@parametrize_idtype
def test_add_edges(idtype):
    # homogeneous graph
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    u = 0
    v = 1
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 3
    u = [0]
    v = [1]
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 4
    u = F.tensor(u, dtype=idtype)
    v = F.tensor(v, dtype=idtype)
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 5
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 0, 0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 1, 1, 1], dtype=idtype))
    g = dgl.add_edges(g, [], [])
    g = dgl.add_edges(g, 0, [])
    g = dgl.add_edges(g, [], 0)
    assert g.device == F.ctx()
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 5
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 0, 0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 1, 1, 1], dtype=idtype))

    # node id larger than current max node id
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    u = F.tensor([0, 1], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    g = dgl.add_edges(g, u, v)
    assert g.number_of_nodes() == 4
    assert g.number_of_edges() == 4
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 1], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 2, 3], dtype=idtype))

    # has data
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.copy_to(F.tensor([1, 1, 1], dtype=idtype), ctx=F.ctx())
    g.edata['h'] = F.copy_to(F.tensor([1, 1], dtype=idtype), ctx=F.ctx())
    u = F.tensor([0, 1], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    e_feat = {'h' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx()),
              'hh' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx())}
    g = dgl.add_edges(g, u, v, e_feat)
    assert g.number_of_nodes() == 4
    assert g.number_of_edges() == 4
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 1], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 2, 3], dtype=idtype))
    assert F.array_equal(g.ndata['h'], F.tensor([1, 1, 1, 0], dtype=idtype))
    assert F.array_equal(g.edata['h'], F.tensor([1, 1, 2, 2], dtype=idtype))
    assert F.array_equal(g.edata['hh'], F.tensor([0, 0, 2, 2], dtype=idtype))

    # zero data graph
    g = dgl.graph(([], []), num_nodes=0, idtype=idtype, device=F.ctx())
    u = F.tensor([0, 1], dtype=idtype)
    v = F.tensor([2, 2], dtype=idtype)
    e_feat = {'h' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx()),
              'hh' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx())}
    g = dgl.add_edges(g, u, v, e_feat)
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 2
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1], dtype=idtype))
    assert F.array_equal(v, F.tensor([2, 2], dtype=idtype))
    assert F.array_equal(g.edata['h'], F.tensor([2, 2], dtype=idtype))
    assert F.array_equal(g.edata['hh'], F.tensor([2, 2], dtype=idtype))

    # bipartite graph
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    u = 0
    v = 1
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes('user') == 2
    assert g.number_of_nodes('game') == 3
    assert g.number_of_edges() == 3
    u = [0]
    v = [1]
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes('user') == 2
    assert g.number_of_nodes('game') == 3
    assert g.number_of_edges() == 4
    u = F.tensor(u, dtype=idtype)
    v = F.tensor(v, dtype=idtype)
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes('user') == 2
    assert g.number_of_nodes('game') == 3
    assert g.number_of_edges() == 5
    u, v = g.edges(form='uv')
    assert F.array_equal(u, F.tensor([0, 1, 0, 0, 0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 1, 1, 1], dtype=idtype))

    # node id larger than current max node id
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    u = F.tensor([0, 2], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    g = dgl.add_edges(g, u, v)
    assert g.device == F.ctx()
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 4
    assert g.number_of_edges() == 4
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 2, 3], dtype=idtype))

    # has data
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h'] = F.copy_to(F.tensor([1, 1], dtype=idtype), ctx=F.ctx())
    g.nodes['game'].data['h'] = F.copy_to(F.tensor([2, 2, 2], dtype=idtype), ctx=F.ctx())
    g.edata['h'] = F.copy_to(F.tensor([1, 1], dtype=idtype), ctx=F.ctx())
    u = F.tensor([0, 2], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    e_feat = {'h' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx()),
              'hh' : F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx())}
    g = dgl.add_edges(g, u, v, e_feat)
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 4
    assert g.number_of_edges() == 4
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1, 0, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([1, 2, 2, 3], dtype=idtype))
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1, 0], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2, 2, 0], dtype=idtype))
    assert F.array_equal(g.edata['h'], F.tensor([1, 1, 2, 2], dtype=idtype))
    assert F.array_equal(g.edata['hh'], F.tensor([0, 0, 2, 2], dtype=idtype))

    # heterogeneous graph
    g = create_test_heterograph3(idtype)
    u = F.tensor([0, 2], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    g = dgl.add_edges(g, u, v, etype='plays')
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 4
    assert g.number_of_nodes('developer') == 2
    assert g.number_of_edges('plays') == 6
    assert g.number_of_edges('develops') == 2
    u, v = g.edges(form='uv', order='eid', etype='plays')
    assert F.array_equal(u, F.tensor([0, 1, 1, 2, 0, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 0, 1, 1, 2, 3], dtype=idtype))
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1, 1], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2, 0, 0], dtype=idtype))
    assert F.array_equal(g.edges['plays'].data['h'], F.tensor([1, 1, 1, 1, 0, 0], dtype=idtype))

    # add with feature
    e_feat = {'h': F.copy_to(F.tensor([2, 2], dtype=idtype), ctx=F.ctx())}
    u = F.tensor([0, 2], dtype=idtype)
    v = F.tensor([2, 3], dtype=idtype)
    g.nodes['game'].data['h'] =  F.copy_to(F.tensor([2, 2, 1, 1], dtype=idtype), ctx=F.ctx())
    g = dgl.add_edges(g, u, v, data=e_feat, etype='develops')
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 4
    assert g.number_of_nodes('developer') == 3
    assert g.number_of_edges('plays') == 6
    assert g.number_of_edges('develops') == 4
    u, v = g.edges(form='uv', order='eid', etype='develops')
    assert F.array_equal(u, F.tensor([0, 1, 0, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 1, 2, 3], dtype=idtype))
    assert F.array_equal(g.nodes['developer'].data['h'], F.tensor([3, 3, 0], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2, 1, 1], dtype=idtype))
    assert F.array_equal(g.edges['develops'].data['h'], F.tensor([0, 0, 2, 2], dtype=idtype))

@parametrize_idtype
def test_add_nodes(idtype):
    # homogeneous Graphs
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.copy_to(F.tensor([1,1,1], dtype=idtype), ctx=F.ctx())
    new_g = dgl.add_nodes(g, 1)
    assert g.number_of_nodes() == 3
    assert new_g.number_of_nodes() == 4
    assert F.array_equal(new_g.ndata['h'], F.tensor([1, 1, 1, 0], dtype=idtype))

    # zero node graph
    g = dgl.graph(([], []), num_nodes=3, idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.copy_to(F.tensor([1,1,1], dtype=idtype), ctx=F.ctx())
    g = dgl.add_nodes(g, 1, data={'h' : F.copy_to(F.tensor([2],  dtype=idtype), ctx=F.ctx())})
    assert g.number_of_nodes() == 4
    assert F.array_equal(g.ndata['h'], F.tensor([1, 1, 1, 2], dtype=idtype))

    # bipartite graph
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    g = dgl.add_nodes(g, 2, data={'h' : F.copy_to(F.tensor([2, 2],  dtype=idtype), ctx=F.ctx())}, ntype='user')
    assert g.number_of_nodes('user') == 4
    assert g.number_of_nodes('game') == 3
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([0, 0, 2, 2], dtype=idtype))
    g = dgl.add_nodes(g, 2, ntype='game')
    assert g.number_of_nodes('user') == 4
    assert g.number_of_nodes('game') == 5

    # heterogeneous graph
    g = create_test_heterograph3(idtype)
    g = dgl.add_nodes(g, 1, ntype='user')
    g = dgl.add_nodes(g, 2, data={'h' : F.copy_to(F.tensor([2, 2],  dtype=idtype), ctx=F.ctx())}, ntype='game')
    assert g.number_of_nodes('user') == 4
    assert g.number_of_nodes('game') == 4
    assert g.number_of_nodes('developer') == 2
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1, 1, 0], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2, 2, 2], dtype=idtype))

@parametrize_idtype
def test_remove_edges(idtype):
    # homogeneous Graphs
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    e = 0
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([2], dtype=idtype))
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    e = [0]
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([2], dtype=idtype))
    e = F.tensor([0], dtype=idtype)
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 0

    # has node data
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.copy_to(F.tensor([1, 2, 3], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_edges(g, 1)
    assert g.number_of_edges() == 1
    assert F.array_equal(g.ndata['h'], F.tensor([1, 2, 3], dtype=idtype))

    # has edge data
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.edata['h'] = F.copy_to(F.tensor([1, 2], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_edges(g, 0)
    assert g.number_of_edges() == 1
    assert F.array_equal(g.edata['h'], F.tensor([2], dtype=idtype))

    # invalid eid
    assert_fail = False
    try:
        g = dgl.remove_edges(g, 1)
    except:
        assert_fail = True
    assert assert_fail

    # bipartite graph
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    e = 0
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([2], dtype=idtype))
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    e = [0]
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([2], dtype=idtype))
    e = F.tensor([0], dtype=idtype)
    g = dgl.remove_edges(g, e)
    assert g.number_of_edges() == 0

    # has data
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h'] = F.copy_to(F.tensor([1, 1], dtype=idtype), ctx=F.ctx())
    g.nodes['game'].data['h'] = F.copy_to(F.tensor([2, 2, 2], dtype=idtype), ctx=F.ctx())
    g.edata['h'] = F.copy_to(F.tensor([1, 2], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_edges(g, 1)
    assert g.number_of_edges() == 1
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2, 2], dtype=idtype))
    assert F.array_equal(g.edata['h'], F.tensor([1], dtype=idtype))

    # heterogeneous graph
    g = create_test_heterograph3(idtype)
    g.edges['plays'].data['h'] = F.copy_to(F.tensor([1, 2, 3, 4], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_edges(g, 1, etype='plays')
    assert g.number_of_edges('plays') == 3
    u, v = g.edges(form='uv', order='eid', etype='plays')
    assert F.array_equal(u, F.tensor([0, 1, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 1, 1], dtype=idtype))
    assert F.array_equal(g.edges['plays'].data['h'], F.tensor([1, 3, 4], dtype=idtype))
    # remove all edges of 'develops'
    g = dgl.remove_edges(g, [0, 1], etype='develops')
    assert g.number_of_edges('develops') == 0
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1, 1], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2, 2], dtype=idtype))
    assert F.array_equal(g.nodes['developer'].data['h'], F.tensor([3, 3], dtype=idtype))

    # batched graph
    ctx = F.ctx()
    g1 = dgl.graph(([0, 1], [1, 2]), num_nodes=5, idtype=idtype, device=ctx)
    g2 = dgl.graph(([], []), idtype=idtype, device=ctx)
    g3 = dgl.graph(([2, 3, 4], [3, 2, 1]), idtype=idtype, device=ctx)
    bg = dgl.batch([g1, g2, g3])
    bg_r = dgl.remove_edges(bg, 2)
    assert bg.batch_size == bg_r.batch_size
    assert F.array_equal(bg.batch_num_nodes(), bg_r.batch_num_nodes())
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([2, 0, 2], dtype=F.int64))

    bg_r = dgl.remove_edges(bg, [0, 2])
    assert bg.batch_size == bg_r.batch_size
    assert F.array_equal(bg.batch_num_nodes(), bg_r.batch_num_nodes())
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([1, 0, 2], dtype=F.int64))

    bg_r = dgl.remove_edges(bg, F.tensor([0, 2], dtype=idtype))
    assert bg.batch_size == bg_r.batch_size
    assert F.array_equal(bg.batch_num_nodes(), bg_r.batch_num_nodes())
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([1, 0, 2], dtype=F.int64))

    # batched heterogeneous graph
    g1 = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1], [1, 2]),
        ('user', 'plays', 'game'): ([1, 3], [0, 1])
    }, num_nodes_dict={'user': 4, 'game': 3}, idtype=idtype, device=ctx)
    g2 = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 2], [3, 4]),
        ('user', 'plays', 'game'): ([], [])
    }, num_nodes_dict={'user': 6, 'game': 2}, idtype=idtype, device=ctx)
    g3 = dgl.heterograph({
        ('user', 'follows', 'user'): ([], []),
        ('user', 'plays', 'game'): ([1, 2], [1, 2])
    }, idtype=idtype, device=ctx)
    bg = dgl.batch([g1, g2, g3])
    bg_r = dgl.remove_edges(bg, 1, etype='follows')
    assert bg.batch_size == bg_r.batch_size
    ntypes = bg.ntypes
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([1, 2, 0], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges('plays'), bg.batch_num_edges('plays'))

    bg_r = dgl.remove_edges(bg, 2, etype='plays')
    assert bg.batch_size == bg_r.batch_size
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([2, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_edges(bg, [0, 1, 3], etype='follows')
    assert bg.batch_size == bg_r.batch_size
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([0, 1, 0], dtype=F.int64))
    assert F.array_equal(bg.batch_num_edges('plays'), bg_r.batch_num_edges('plays'))

    bg_r = dgl.remove_edges(bg, [1, 2], etype='plays')
    assert bg.batch_size == bg_r.batch_size
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_edges(bg, F.tensor([0, 1, 3], dtype=idtype), etype='follows')
    assert bg.batch_size == bg_r.batch_size
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([0, 1, 0], dtype=F.int64))
    assert F.array_equal(bg.batch_num_edges('plays'), bg_r.batch_num_edges('plays'))

    bg_r = dgl.remove_edges(bg, F.tensor([1, 2], dtype=idtype), etype='plays')
    assert bg.batch_size == bg_r.batch_size
    for nty in ntypes:
        assert F.array_equal(bg.batch_num_nodes(nty), bg_r.batch_num_nodes(nty))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

@parametrize_idtype
def test_remove_nodes(idtype):
    # homogeneous Graphs
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    n = 0
    g = dgl.remove_nodes(g, n)
    assert g.number_of_nodes() == 2
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1], dtype=idtype))
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    n = [1]
    g = dgl.remove_nodes(g, n)
    assert g.number_of_nodes() == 2
    assert g.number_of_edges() == 0
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    n = F.tensor([2], dtype=idtype)
    g = dgl.remove_nodes(g, n)
    assert g.number_of_nodes() == 2
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1], dtype=idtype))

    # invalid nid
    assert_fail = False
    try:
        g.remove_nodes(3)
    except:
        assert_fail = True
    assert assert_fail

    # has node and edge data
    g = dgl.graph(([0, 0, 2], [0, 1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['hv'] = F.copy_to(F.tensor([1, 2, 3], dtype=idtype), ctx=F.ctx())
    g.edata['he'] = F.copy_to(F.tensor([1, 2, 3], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_nodes(g, F.tensor([0], dtype=idtype))
    assert g.number_of_nodes() == 2
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([1], dtype=idtype))
    assert F.array_equal(g.ndata['hv'], F.tensor([2, 3], dtype=idtype))
    assert F.array_equal(g.edata['he'], F.tensor([3], dtype=idtype))

    # node id larger than current max node id
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    n = 0
    g = dgl.remove_nodes(g, n, ntype='user')
    assert g.number_of_nodes('user') == 1
    assert g.number_of_nodes('game') == 3
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0], dtype=idtype))
    assert F.array_equal(v, F.tensor([2], dtype=idtype))
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    n = [1]
    g = dgl.remove_nodes(g, n, ntype='user')
    assert g.number_of_nodes('user') == 1
    assert g.number_of_nodes('game') == 3
    assert g.number_of_edges() == 1
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0], dtype=idtype))
    assert F.array_equal(v, F.tensor([1], dtype=idtype))
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
    n = F.tensor([0], dtype=idtype)
    g = dgl.remove_nodes(g, n, ntype='game')
    assert g.number_of_nodes('user') == 2
    assert g.number_of_nodes('game') == 2
    assert g.number_of_edges() == 2
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 1], dtype=idtype))
    assert F.array_equal(v, F.tensor([0 ,1], dtype=idtype))

    # heterogeneous graph
    g = create_test_heterograph3(idtype)
    g.edges['plays'].data['h'] = F.copy_to(F.tensor([1, 2, 3, 4], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_nodes(g, 0, ntype='game')
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 1
    assert g.number_of_nodes('developer') == 2
    assert g.number_of_edges('plays') == 2
    assert g.number_of_edges('develops') == 1
    assert F.array_equal(g.nodes['user'].data['h'], F.tensor([1, 1, 1], dtype=idtype))
    assert F.array_equal(g.nodes['game'].data['h'], F.tensor([2], dtype=idtype))
    assert F.array_equal(g.nodes['developer'].data['h'], F.tensor([3, 3], dtype=idtype))
    u, v = g.edges(form='uv', order='eid', etype='plays')
    assert F.array_equal(u, F.tensor([1, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 0], dtype=idtype))
    assert F.array_equal(g.edges['plays'].data['h'], F.tensor([3, 4], dtype=idtype))
    u, v = g.edges(form='uv', order='eid', etype='develops')
    assert F.array_equal(u, F.tensor([1], dtype=idtype))
    assert F.array_equal(v, F.tensor([0], dtype=idtype))

    # batched graph
    ctx = F.ctx()
    g1 = dgl.graph(([0, 1], [1, 2]), num_nodes=5, idtype=idtype, device=ctx)
    g2 = dgl.graph(([], []), idtype=idtype, device=ctx)
    g3 = dgl.graph(([2, 3, 4], [3, 2, 1]), idtype=idtype, device=ctx)
    bg = dgl.batch([g1, g2, g3])
    bg_r = dgl.remove_nodes(bg, 1)
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes(), F.tensor([4, 0, 5], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([0, 0, 3], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, [1, 7])
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes(), F.tensor([4, 0, 4], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([0, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, F.tensor([1, 7], dtype=idtype))
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes(), F.tensor([4, 0, 4], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges(), F.tensor([0, 0, 1], dtype=F.int64))

    # batched heterogeneous graph
    g1 = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1], [1, 2]),
        ('user', 'plays', 'game'): ([1, 3], [0, 1])
    }, num_nodes_dict={'user': 4, 'game': 3}, idtype=idtype, device=ctx)
    g2 = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 2], [3, 4]),
        ('user', 'plays', 'game'): ([], [])
    }, num_nodes_dict={'user': 6, 'game': 2}, idtype=idtype, device=ctx)
    g3 = dgl.heterograph({
        ('user', 'follows', 'user'): ([], []),
        ('user', 'plays', 'game'): ([1, 2], [1, 2])
    }, idtype=idtype, device=ctx)
    bg = dgl.batch([g1, g2, g3])
    bg_r = dgl.remove_nodes(bg, 1, ntype='user')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes('user'), F.tensor([3, 6, 3], dtype=F.int64))
    assert F.array_equal(bg.batch_num_nodes('game'), bg_r.batch_num_nodes('game'))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([0, 2, 0], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 2], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, 6, ntype='game')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg.batch_num_nodes('user'), bg_r.batch_num_nodes('user'))
    assert F.array_equal(bg_r.batch_num_nodes('game'), F.tensor([3, 2, 2], dtype=F.int64))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([2, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, [1, 5, 6, 11], ntype='user')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes('user'), F.tensor([3, 4, 2], dtype=F.int64))
    assert F.array_equal(bg.batch_num_nodes('game'), bg_r.batch_num_nodes('game'))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([0, 1, 0], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, [0, 3, 4, 7], ntype='game')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg.batch_num_nodes('user'), bg_r.batch_num_nodes('user'))
    assert F.array_equal(bg_r.batch_num_nodes('game'), F.tensor([2, 0, 2], dtype=F.int64))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, F.tensor([1, 5, 6, 11], dtype=idtype), ntype='user')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg_r.batch_num_nodes('user'), F.tensor([3, 4, 2], dtype=F.int64))
    assert F.array_equal(bg.batch_num_nodes('game'), bg_r.batch_num_nodes('game'))
    assert F.array_equal(bg_r.batch_num_edges('follows'), F.tensor([0, 1, 0], dtype=F.int64))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

    bg_r = dgl.remove_nodes(bg, F.tensor([0, 3, 4, 7], dtype=idtype), ntype='game')
    assert bg_r.batch_size == bg.batch_size
    assert F.array_equal(bg.batch_num_nodes('user'), bg_r.batch_num_nodes('user'))
    assert F.array_equal(bg_r.batch_num_nodes('game'), F.tensor([2, 0, 2], dtype=F.int64))
    assert F.array_equal(bg.batch_num_edges('follows'), bg_r.batch_num_edges('follows'))
    assert F.array_equal(bg_r.batch_num_edges('plays'), F.tensor([1, 0, 1], dtype=F.int64))

@parametrize_idtype
def test_add_selfloop(idtype):
    # homogeneous graph
    g = dgl.graph(([0, 0, 2], [2, 1, 0]), idtype=idtype, device=F.ctx())
    g.edata['he'] = F.copy_to(F.tensor([1, 2, 3], dtype=idtype), ctx=F.ctx())
    g.ndata['hn'] = F.copy_to(F.tensor([1, 2, 3], dtype=idtype), ctx=F.ctx())
    g = dgl.add_self_loop(g)
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 6
    u, v = g.edges(form='uv', order='eid')
    assert F.array_equal(u, F.tensor([0, 0, 2, 0, 1, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([2, 1, 0, 0, 1, 2], dtype=idtype))
    assert F.array_equal(g.edata['he'], F.tensor([1, 2, 3, 0, 0, 0], dtype=idtype))

    # bipartite graph
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1, 2], [1, 2, 2])}, idtype=idtype, device=F.ctx())
    # nothing will happend
    raise_error = False
    try:
        g = dgl.add_self_loop(g)
    except:
        raise_error = True
    assert raise_error

    g = create_test_heterograph5(idtype)
    g = dgl.add_self_loop(g, etype='follows')
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 2
    assert g.number_of_edges('follows') == 5
    assert g.number_of_edges('plays') == 2
    u, v = g.edges(form='uv', order='eid', etype='follows')
    assert F.array_equal(u, F.tensor([1, 2, 0, 1, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 1, 0, 1, 2], dtype=idtype))
    assert F.array_equal(g.edges['follows'].data['h'], F.tensor([1, 2, 0, 0, 0], dtype=idtype))
    assert F.array_equal(g.edges['plays'].data['h'], F.tensor([1, 2], dtype=idtype))

    raise_error = False
    try:
        g = dgl.add_self_loop(g, etype='plays')
    except:
        raise_error = True
    assert raise_error

@parametrize_idtype
def test_remove_selfloop(idtype):
    # homogeneous graph
    g = dgl.graph(([0, 0, 0, 1], [1, 0, 0, 2]), idtype=idtype, device=F.ctx())
    g.edata['he'] = F.copy_to(F.tensor([1, 2, 3, 4], dtype=idtype), ctx=F.ctx())
    g = dgl.remove_self_loop(g)
    assert g.number_of_nodes() == 3
    assert g.number_of_edges() == 2
    assert F.array_equal(g.edata['he'], F.tensor([1, 4], dtype=idtype))

    # bipartite graph
    g = dgl.heterograph(
        {('user', 'plays', 'game'): ([0, 1, 2], [1, 2, 2])}, idtype=idtype, device=F.ctx())
    # nothing will happend
    raise_error = False
    try:
        g = dgl.remove_self_loop(g, etype='plays')
    except:
        raise_error = True
    assert raise_error

    g = create_test_heterograph4(idtype)
    g = dgl.remove_self_loop(g, etype='follows')
    assert g.number_of_nodes('user') == 3
    assert g.number_of_nodes('game') == 2
    assert g.number_of_edges('follows') == 2
    assert g.number_of_edges('plays') == 2
    u, v = g.edges(form='uv', order='eid', etype='follows')
    assert F.array_equal(u, F.tensor([1, 2], dtype=idtype))
    assert F.array_equal(v, F.tensor([0, 1], dtype=idtype))
    assert F.array_equal(g.edges['follows'].data['h'], F.tensor([2, 4], dtype=idtype))
    assert F.array_equal(g.edges['plays'].data['h'], F.tensor([1, 2], dtype=idtype))

    raise_error = False
    try:
        g = dgl.remove_self_loop(g, etype='plays')
    except:
        raise_error = True
    assert raise_error


@parametrize_idtype
def test_reorder_graph(idtype):
    g = dgl.graph(([0, 1, 2, 3, 4], [2, 2, 3, 2, 3]),
                  idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.copy_to(F.randn((g.num_nodes(), 3)), ctx=F.ctx())
    g.edata['w'] = F.copy_to(F.randn((g.num_edges(), 2)), ctx=F.ctx())

    # call with default: node_permute_algo=None, edge_permute_algo='src'
    rg = dgl.reorder_graph(g)
    assert dgl.EID in rg.edata.keys()
    src = F.asnumpy(rg.edges()[0])
    assert np.array_equal(src, np.sort(src))

    # call with 'rcmk' node_permute_algo
    rg = dgl.reorder_graph(g, node_permute_algo='rcmk')
    assert dgl.NID in rg.ndata.keys()
    assert dgl.EID in rg.edata.keys()
    src = F.asnumpy(rg.edges()[0])
    assert np.array_equal(src, np.sort(src))

    # call with 'dst' edge_permute_algo
    rg = dgl.reorder_graph(g, edge_permute_algo='dst')
    dst = F.asnumpy(rg.edges()[1])
    assert np.array_equal(dst, np.sort(dst))

    # call with unknown edge_permute_algo
    raise_error = False
    try:
        dgl.reorder_graph(g, edge_permute_algo='none')
    except:
        raise_error = True
    assert raise_error

    # reorder back to original according to stored ids
    rg = dgl.reorder_graph(g, node_permute_algo='rcmk')
    rg2 = dgl.reorder_graph(rg, 'custom', permute_config={
        'nodes_perm': np.argsort(F.asnumpy(rg.ndata[dgl.NID]))})
    assert F.array_equal(g.ndata['h'], rg2.ndata['h'])
    assert F.array_equal(g.edata['w'], rg2.edata['w'])

    # do not store ids
    rg = dgl.reorder_graph(g, store_ids=False)
    assert not dgl.NID in rg.ndata.keys()
    assert not dgl.EID in rg.edata.keys()

    # metis does not work on windows.
    if os.name == 'nt':
        pass
    else:
        # metis_partition may fail for small graph.
        mg = create_large_graph(1000).to(F.ctx())

        # call with metis strategy, but k is not specified
        raise_error = False
        try:
            dgl.reorder_graph(mg, node_permute_algo='metis')
        except:
            raise_error = True
        assert raise_error

        # call with metis strategy, k is specified
        raise_error = False
        try:
            dgl.reorder_graph(mg,
                              node_permute_algo='metis', permute_config={'k': 2})
        except:
            raise_error = True
        assert not raise_error

    # call with qualified nodes_perm specified
    nodes_perm = np.random.permutation(g.num_nodes())
    raise_error = False
    try:
        dgl.reorder_graph(g, node_permute_algo='custom', permute_config={
            'nodes_perm': nodes_perm})
    except:
        raise_error = True
    assert not raise_error

    # call with unqualified nodes_perm specified
    raise_error = False
    try:
        dgl.reorder_graph(g, node_permute_algo='custom', permute_config={
            'nodes_perm':  nodes_perm[:g.num_nodes() - 1]})
    except:
        raise_error = True
    assert raise_error

    # call with unsupported strategy
    raise_error = False
    try:
        dgl.reorder_graph(g, node_permute_algo='cmk')
    except:
        raise_error = True
    assert raise_error

    # heterograph: not supported
    raise_error = False
    try:
        hg = dgl.heterogrpah({('user', 'follow', 'user'): (
            [0, 1], [1, 2])}, idtype=idtype, device=F.ctx())
        dgl.reorder_graph(hg)
    except:
        raise_error = True
    assert raise_error

    # TODO: shall we fix them?
    # add 'csc' format if needed
    #fg = g.formats('csr')
    #assert 'csc' not in sum(fg.formats().values(), [])
    #rfg = dgl.reorder_graph(fg)
    #assert 'csc' in sum(rfg.formats().values(), [])

@unittest.skipIf(dgl.backend.backend_name == "tensorflow", reason="TF doesn't support a slicing operation")
@parametrize_idtype
def test_norm_by_dst(idtype):
    # Case1: A homogeneous graph
    g = dgl.graph(([0, 1, 1], [1, 1, 2]), idtype=idtype, device=F.ctx())
    eweight = dgl.norm_by_dst(g)
    assert F.allclose(eweight, F.tensor([0.5, 0.5, 1.0]))

    # Case2: A heterogeneous graph
    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1], [1, 2]),
        ('user', 'plays', 'game'): ([0, 1, 1], [1, 1, 2])
    }, idtype=idtype, device=F.ctx())
    eweight = dgl.norm_by_dst(g, etype=('user', 'plays', 'game'))
    assert F.allclose(eweight, F.tensor([0.5, 0.5, 1.0]))

@parametrize_idtype
def test_module_add_self_loop(idtype):
    g = dgl.graph(([1, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 2))
    g.edata['w'] = F.randn((g.num_edges(), 3))

    # Case1: add self-loops with the default setting
    transform = dgl.AddSelfLoop()
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_nodes()
    assert new_g.num_edges() == 4
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (1, 1), (1, 2), (2, 2)}
    assert 'h' in new_g.ndata
    assert 'w' in new_g.edata

    # Case2: Remove self-loops first to avoid duplicate ones
    transform = dgl.AddSelfLoop(allow_duplicate=True)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_nodes()
    assert new_g.num_edges() == 5
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (1, 1), (1, 2), (2, 2)}
    assert 'h' in new_g.ndata
    assert 'w' in new_g.edata

    # Create a heterogeneous graph
    g = dgl.heterograph({
        ('user', 'plays', 'game'): ([0], [1]),
        ('user', 'follows', 'user'): ([1], [3])
    }, idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h1'] = F.randn((4, 2))
    g.edges['plays'].data['w1'] = F.randn((1, 3))
    g.nodes['game'].data['h2'] = F.randn((2, 4))
    g.edges['follows'].data['w2'] = F.randn((1, 5))

    # Case3: add self-loops for a heterogeneous graph
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.ntypes == g.ntypes
    assert new_g.canonical_etypes == g.canonical_etypes
    for nty in new_g.ntypes:
        assert new_g.num_nodes(nty) == g.num_nodes(nty)
    assert new_g.num_edges('plays') == 1
    assert new_g.num_edges('follows') == 5
    assert 'h1' in new_g.nodes['user'].data
    assert 'h2' in new_g.nodes['game'].data
    assert 'w1' in new_g.edges['plays'].data
    assert 'w2' in new_g.edges['follows'].data

    # Case4: add self-etypes for a heterogeneous graph
    transform = dgl.AddSelfLoop(new_etypes=True)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.ntypes == g.ntypes
    assert set(new_g.canonical_etypes) == {
        ('user', 'plays', 'game'), ('user', 'follows', 'user'),
        ('user', 'self', 'user'), ('game', 'self', 'game')
    }
    for nty in new_g.ntypes:
        assert new_g.num_nodes(nty) == g.num_nodes(nty)
    assert new_g.num_edges('plays') == 1
    assert new_g.num_edges('follows') == 5
    assert new_g.num_edges(('user', 'self', 'user')) == 4
    assert new_g.num_edges(('game', 'self', 'game')) == 2
    assert 'h1' in new_g.nodes['user'].data
    assert 'h2' in new_g.nodes['game'].data
    assert 'w1' in new_g.edges['plays'].data
    assert 'w2' in new_g.edges['follows'].data

@parametrize_idtype
def test_module_remove_self_loop(idtype):
    transform = dgl.RemoveSelfLoop()

    # Case1: homogeneous graph
    g = dgl.graph(([1, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 2))
    g.edata['w'] = F.randn((g.num_edges(), 3))
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_nodes()
    assert new_g.num_edges() == 1
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(1, 2)}
    assert 'h' in new_g.ndata
    assert 'w' in new_g.edata

    # Case2: heterogeneous graph
    g = dgl.heterograph({
        ('user', 'plays', 'game'): ([0, 1], [1, 1]),
        ('user', 'follows', 'user'): ([1, 2], [2, 2])
    }, idtype=idtype, device=F.ctx())
    g.nodes['user'].data['h1'] = F.randn((3, 2))
    g.edges['plays'].data['w1'] = F.randn((2, 3))
    g.nodes['game'].data['h2'] = F.randn((2, 4))
    g.edges['follows'].data['w2'] = F.randn((2, 5))

    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.ntypes == g.ntypes
    assert new_g.canonical_etypes == g.canonical_etypes
    for nty in new_g.ntypes:
        assert new_g.num_nodes(nty) == g.num_nodes(nty)
    assert new_g.num_edges('plays') == 2
    assert new_g.num_edges('follows') == 1
    assert 'h1' in new_g.nodes['user'].data
    assert 'h2' in new_g.nodes['game'].data
    assert 'w1' in new_g.edges['plays'].data
    assert 'w2' in new_g.edges['follows'].data

@parametrize_idtype
def test_module_add_reverse(idtype):
    transform = dgl.AddReverse()

    # Case1: Add reverse edges for a homogeneous graph
    g = dgl.graph(([0], [1]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 3))
    g.edata['w'] = F.randn((g.num_edges(), 2))
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert g.num_nodes() == new_g.num_nodes()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 0)}
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    assert F.allclose(g.edata['w'], F.narrow_row(new_g.edata['w'], 0, 1))
    assert F.allclose(F.narrow_row(new_g.edata['w'], 1, 2), F.zeros((1, 2), F.float32, F.ctx()))

    # Case2: Add reverse edges for a homogeneous graph and copy edata
    transform = dgl.AddReverse(copy_edata=True)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert g.num_nodes() == new_g.num_nodes()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 0)}
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    assert F.allclose(g.edata['w'], F.narrow_row(new_g.edata['w'], 0, 1))
    assert F.allclose(g.edata['w'], F.narrow_row(new_g.edata['w'], 1, 2))

    # Case3: Add reverse edges for a heterogeneous graph
    g = dgl.heterograph({
        ('user', 'plays', 'game'): ([0, 1], [1, 1]),
        ('user', 'follows', 'user'): ([1, 2], [2, 2])
    }, device=F.ctx())
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert g.ntypes == new_g.ntypes
    assert set(new_g.canonical_etypes) == {
        ('user', 'plays', 'game'), ('user', 'follows', 'user'), ('game', 'rev_plays', 'user')}
    for nty in g.ntypes:
        assert g.num_nodes(nty) == new_g.num_nodes(nty)

    src, dst = new_g.edges(etype='plays')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 1)}

    src, dst = new_g.edges(etype='follows')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(1, 2), (2, 2), (2, 1)}

    src, dst = new_g.edges(etype='rev_plays')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(1, 1), (1, 0)}

    # Case4: Enforce reverse edge types for symmetric canonical edge types
    transform = dgl.AddReverse(sym_new_etype=True)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert g.ntypes == new_g.ntypes
    assert set(new_g.canonical_etypes) == {
        ('user', 'plays', 'game'), ('user', 'follows', 'user'),
        ('game', 'rev_plays', 'user'), ('user', 'rev_follows', 'user')}
    for nty in g.ntypes:
        assert g.num_nodes(nty) == new_g.num_nodes(nty)

    src, dst = new_g.edges(etype='plays')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 1)}

    src, dst = new_g.edges(etype='follows')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(1, 2), (2, 2)}

    src, dst = new_g.edges(etype='rev_plays')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(1, 1), (1, 0)}

    src, dst = new_g.edges(etype='rev_follows')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(2, 1), (2, 2)}

@unittest.skipIf(F._default_context_str == 'gpu', reason="GPU not supported for to_simple")
@parametrize_idtype
def test_module_to_simple(idtype):
    transform = dgl.ToSimple()
    g = dgl.graph(([0, 1, 1], [1, 2, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 2))
    g.edata['w'] = F.tensor([[0.1], [0.2], [0.3]])
    sg = transform(g)
    assert sg.device == g.device
    assert sg.idtype == g.idtype
    assert sg.num_nodes() == g.num_nodes()
    assert sg.num_edges() == 2
    src, dst = sg.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 2)}
    assert F.allclose(sg.edata['count'], F.tensor([1, 2]))
    assert F.allclose(sg.ndata['h'], g.ndata['h'])

    g = dgl.heterograph({
        ('user', 'follows', 'user'): ([0, 1, 1], [1, 2, 2]),
        ('user', 'plays', 'game'): ([0, 1, 0], [1, 1, 1])
    })
    sg = transform(g)
    assert sg.device == g.device
    assert sg.idtype == g.idtype
    assert sg.ntypes == g.ntypes
    assert sg.canonical_etypes == g.canonical_etypes
    for nty in sg.ntypes:
        assert sg.num_nodes(nty) == g.num_nodes(nty)
    for ety in sg.canonical_etypes:
        assert sg.num_edges(ety) == 2

    src, dst = sg.edges(etype='follows')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 2)}

    src, dst = sg.edges(etype='plays')
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 1)}

@parametrize_idtype
def test_module_line_graph(idtype):
    transform = dgl.LineGraph()
    g = dgl.graph(([0, 1, 1], [1, 0, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.tensor([[0.], [1.], [2.]])
    g.edata['w'] = F.tensor([[0.], [0.1], [0.2]])
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_edges()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (0, 2), (1, 0)}

    transform = dgl.LineGraph(backtracking=False)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_edges()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 2)}

@parametrize_idtype
def test_module_khop_graph(idtype):
    transform = dgl.KHopGraph(2)
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 2))
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_nodes() == g.num_nodes()
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 2)}

@parametrize_idtype
def test_module_add_metapaths(idtype):
    g = dgl.heterograph({
        ('person', 'author', 'paper'): ([0, 0, 1], [1, 2, 2]),
        ('paper', 'accepted', 'venue'): ([1], [0]),
        ('paper', 'rejected', 'venue'): ([2], [1])
    }, idtype=idtype, device=F.ctx())
    g.nodes['venue'].data['h'] = F.randn((g.num_nodes('venue'), 2))
    g.edges['author'].data['h'] = F.randn((g.num_edges('author'), 3))

    # Case1: keep_orig_edges is True
    metapaths = {
        'accepted': [('person', 'author', 'paper'), ('paper', 'accepted', 'venue')],
        'rejected': [('person', 'author', 'paper'), ('paper', 'rejected', 'venue')]
    }
    transform = dgl.AddMetaPaths(metapaths)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.ntypes == g.ntypes
    assert set(new_g.canonical_etypes) == {
        ('person', 'author', 'paper'), ('paper', 'accepted', 'venue'),
        ('paper', 'rejected', 'venue'), ('person', 'accepted', 'venue'),
        ('person', 'rejected', 'venue')
    }
    for nty in new_g.ntypes:
        assert new_g.num_nodes(nty) == g.num_nodes(nty)
    for ety in g.canonical_etypes:
        assert new_g.num_edges(ety) == g.num_edges(ety)
    assert F.allclose(g.nodes['venue'].data['h'], new_g.nodes['venue'].data['h'])
    assert F.allclose(g.edges['author'].data['h'], new_g.edges['author'].data['h'])

    src, dst = new_g.edges(etype=('person', 'accepted', 'venue'))
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0)}

    src, dst = new_g.edges(etype=('person', 'rejected', 'venue'))
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 1)}

    # Case2: keep_orig_edges is False
    transform = dgl.AddMetaPaths(metapaths, keep_orig_edges=False)
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.ntypes == g.ntypes
    assert len(new_g.canonical_etypes) == 2
    for nty in new_g.ntypes:
        assert new_g.num_nodes(nty) == g.num_nodes(nty)
    assert F.allclose(g.nodes['venue'].data['h'], new_g.nodes['venue'].data['h'])

    src, dst = new_g.edges(etype=('person', 'accepted', 'venue'))
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0)}

    src, dst = new_g.edges(etype=('person', 'rejected', 'venue'))
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 1)}

@parametrize_idtype
def test_module_compose(idtype):
    g = dgl.graph(([0, 1], [1, 2]), idtype=idtype, device=F.ctx())
    transform = dgl.Compose([dgl.AddReverse(), dgl.AddSelfLoop()])
    new_g = transform(g)
    assert new_g.device == g.device
    assert new_g.idtype == g.idtype
    assert new_g.num_edges() == 7

    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 1), (1, 2), (1, 0), (2, 1), (0, 0), (1, 1), (2, 2)}

@parametrize_idtype
def test_module_gcnnorm(idtype):
    g = dgl.heterograph({
        ('A', 'r1', 'A'): ([0, 1, 2], [0, 0, 1]),
        ('A', 'r2', 'B'): ([0, 0], [1, 1]),
        ('B', 'r3', 'B'): ([0, 1, 2], [0, 0, 1])
    }, idtype=idtype, device=F.ctx())
    g.edges['r3'].data['w'] = F.tensor([0.1, 0.2, 0.3])
    transform = dgl.GCNNorm()
    new_g = transform(g)
    assert 'w' not in new_g.edges[('A', 'r2', 'B')].data
    assert F.allclose(new_g.edges[('A', 'r1', 'A')].data['w'],
                      F.tensor([1./2, 1./math.sqrt(2), 0.]))
    assert F.allclose(new_g.edges[('B', 'r3', 'B')].data['w'], F.tensor([1./3, 2./3, 0.]))

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_ppr(idtype):
    g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((6, 2))
    transform = dgl.PPR(avg_degree=2)
    new_g = transform(g)
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.num_nodes() == g.num_nodes()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (0, 2), (0, 4), (1, 1), (1, 3), (1, 5), (2, 2),
                    (2, 3), (2, 4), (3, 3), (3, 5), (4, 3), (4, 4), (4, 5), (5, 5)}
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    assert 'w' in new_g.edata

    # Prior edge weights
    g.edata['w'] = F.tensor([0.1, 0.2, 0.3, 0.4, 0.5])
    new_g = transform(g)
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (2, 4),
                    (3, 3), (3, 5), (4, 3), (4, 4), (4, 5), (5, 5)}

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_heat_kernel(idtype):
    # Case1: directed graph
    g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((6, 2))
    transform = dgl.HeatKernel(avg_degree=1)
    new_g = transform(g)
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.num_nodes() == g.num_nodes()
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    assert 'w' in new_g.edata

    # Case2: weighted undirected graph
    g = dgl.graph(([0, 1, 2, 3], [1, 0, 3, 2]), idtype=idtype, device=F.ctx())
    g.edata['w'] = F.tensor([0.1, 0.2, 0.3, 0.4])
    new_g = transform(g)
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (1, 1), (2, 2), (3, 3)}

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_gdc(idtype):
    transform = dgl.GDC([0.1, 0.2, 0.1], avg_degree=1)
    g = dgl.graph(([0, 1, 2, 3, 4], [2, 3, 4, 5, 3]), idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((6, 2))
    new_g = transform(g)
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.num_nodes() == g.num_nodes()
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (0, 2), (0, 4), (1, 1), (1, 3), (1, 5), (2, 2), (2, 3),
                    (2, 4), (3, 3), (3, 5), (4, 3), (4, 4), (4, 5), (5, 5)}
    assert F.allclose(g.ndata['h'], new_g.ndata['h'])
    assert 'w' in new_g.edata

    # Prior edge weights
    g.edata['w'] = F.tensor([0.1, 0.2, 0.3, 0.4, 0.5])
    new_g = transform(g)
    src, dst = new_g.edges()
    eset = set(zip(list(F.asnumpy(src)), list(F.asnumpy(dst))))
    assert eset == {(0, 0), (1, 1), (2, 2), (3, 3), (4, 3), (4, 4), (5, 5)}

@parametrize_idtype
def test_module_node_shuffle(idtype):
    transform = dgl.NodeShuffle()
    g = dgl.heterograph({
        ('A', 'r', 'B'): ([0, 1], [1, 2]),
    }, idtype=idtype, device=F.ctx())
    new_g = transform(g)

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_drop_node(idtype):
    transform = dgl.DropNode()
    g = dgl.heterograph({
        ('A', 'r', 'B'): ([0, 1], [1, 2]),
    }, idtype=idtype, device=F.ctx())
    new_g = transform(g)
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.ntypes == g.ntypes
    assert new_g.canonical_etypes == g.canonical_etypes

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_drop_edge(idtype):
    transform = dgl.DropEdge()
    g = dgl.heterograph({
        ('A', 'r1', 'B'): ([0, 1], [1, 2]),
        ('C', 'r2', 'C'): ([3, 4, 5], [6, 7, 8])
    }, idtype=idtype, device=F.ctx())
    new_g = transform(g)
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.ntypes == g.ntypes
    assert new_g.canonical_etypes == g.canonical_etypes

@parametrize_idtype
def test_module_add_edge(idtype):
    transform = dgl.AddEdge()
    g = dgl.heterograph({
        ('A', 'r1', 'B'): ([0, 1, 2, 3, 4], [1, 2, 3, 4, 5]),
        ('C', 'r2', 'C'): ([0, 1, 2, 3, 4], [1, 2, 3, 4, 5])
    }, idtype=idtype, device=F.ctx())
    new_g = transform(g)
    assert new_g.num_edges(('A', 'r1', 'B')) == 6
    assert new_g.num_edges(('C', 'r2', 'C')) == 6
    assert new_g.idtype == g.idtype
    assert new_g.device == g.device
    assert new_g.ntypes == g.ntypes
    assert new_g.canonical_etypes == g.canonical_etypes

@parametrize_idtype
def test_module_random_walk_pe(idtype):
    transform = dgl.RandomWalkPE(2, 'rwpe')
    g = dgl.graph(([0, 1, 1], [1, 1, 0]), idtype=idtype, device=F.ctx())
    new_g = transform(g)
    tgt = F.copy_to(F.tensor([[0., 0.5],[0.5, 0.75]]), g.device)
    assert F.allclose(new_g.ndata['rwpe'], tgt)

@parametrize_idtype
def test_module_laplacian_pe(idtype):
    transform = dgl.LaplacianPE(2, 'lappe')
    g = dgl.graph(([2, 1, 0, 3, 1, 1],[3, 0, 1, 3, 3, 1]), idtype=idtype, device=F.ctx())
    new_g = transform(g)
    tgt = F.copy_to(F.tensor([[ 0.24971116, 0.],
        [ 0.11771496, 0.],
        [ 0.83237050, 1.],
        [ 0.48056933, 0.]]), g.device)
    # tensorflow has no abs() api
    if dgl.backend.backend_name == 'tensorflow':
        assert F.allclose(new_g.ndata['lappe'].__abs__(), tgt)
    # pytorch & mxnet
    else:
        assert F.allclose(new_g.ndata['lappe'].abs(), tgt)

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@pytest.mark.parametrize('g', get_cases(['has_scalar_e_feature']))
def test_module_sign(g):
    import torch

    ctx = F.ctx()
    g = g.to(ctx)
    adj = g.adj(transpose=True, scipy_fmt='coo').todense()
    adj = torch.tensor(adj).float().to(ctx)

    weight_adj = g.adj(transpose=True, scipy_fmt='coo').astype(float).todense()
    weight_adj = torch.tensor(weight_adj).float().to(ctx)
    src, dst = g.edges()
    src, dst = src.long(), dst.long()
    weight_adj[dst, src] = g.edata['scalar_w']

    # raw
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', diffuse_op='raw')
    g = transform(g)
    assert torch.allclose(g.ndata['out_feat_1'], torch.matmul(adj, g.ndata['h']))

    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', eweight_name='scalar_w', diffuse_op='raw')
    g = transform(g)
    assert torch.allclose(g.ndata['out_feat_1'], torch.matmul(weight_adj, g.ndata['h']))

    # rw
    adj_rw = torch.matmul(torch.diag(1 / adj.sum(dim=1)), adj)
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', diffuse_op='rw')
    g = transform(g)
    assert torch.allclose(g.ndata['out_feat_1'], torch.matmul(adj_rw, g.ndata['h']))

    weight_adj_rw = torch.matmul(torch.diag(1 / weight_adj.sum(dim=1)), weight_adj)
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', eweight_name='scalar_w', diffuse_op='rw')
    g = transform(g)
    assert torch.allclose(g.ndata['out_feat_1'], torch.matmul(weight_adj_rw, g.ndata['h']))

    # gcn
    raw_eweight = g.edata['scalar_w']
    gcn_norm = dgl.GCNNorm()
    g = gcn_norm(g)
    adj_gcn = adj.clone()
    adj_gcn[dst, src] = g.edata.pop('w')
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', diffuse_op='gcn')
    g = transform(g)
    target = torch.matmul(adj_gcn, g.ndata['h'])
    assert torch.allclose(g.ndata['out_feat_1'], target)

    gcn_norm = dgl.GCNNorm('scalar_w')
    g = gcn_norm(g)
    weight_adj_gcn = weight_adj.clone()
    weight_adj_gcn[dst, src] = g.edata['scalar_w']
    g.edata['scalar_w'] = raw_eweight
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h',
                                  eweight_name='scalar_w', diffuse_op='gcn')
    g = transform(g)
    target = torch.matmul(weight_adj_gcn, g.ndata['h'])
    assert torch.allclose(g.ndata['out_feat_1'], target)

    # ppr
    alpha = 0.2
    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', diffuse_op='ppr', alpha=alpha)
    g = transform(g)
    target = (1 - alpha) * torch.matmul(adj_gcn, g.ndata['h']) + alpha * g.ndata['h']
    assert torch.allclose(g.ndata['out_feat_1'], target)

    transform = dgl.SIGNDiffusion(k=1, in_feat_name='h', eweight_name='scalar_w',
                                  diffuse_op='ppr', alpha=alpha)
    g = transform(g)
    target = (1 - alpha) * torch.matmul(weight_adj_gcn, g.ndata['h']) + alpha * g.ndata['h']
    assert torch.allclose(g.ndata['out_feat_1'], target)

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_row_feat_normalizer(idtype):
    # Case1: Normalize features of a homogeneous graph.
    transform = dgl.RowFeatNormalizer(subtract_min=True,
                                      node_feat_names=['h'], edge_feat_names=['w'])
    g = dgl.rand_graph(5, 5, idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.randn((g.num_nodes(), 128))
    g.edata['w'] = F.randn((g.num_edges(), 128))
    g = transform(g)
    assert g.ndata['h'].shape == (g.num_nodes(), 128)
    assert g.edata['w'].shape == (g.num_edges(), 128)
    assert F.allclose(g.ndata['h'].sum(1), F.tensor([1.0, 1.0, 1.0, 1.0, 1.0]))
    assert F.allclose(g.edata['w'].sum(1), F.tensor([1.0, 1.0, 1.0, 1.0, 1.0]))

    # Case2: Normalize features of a heterogeneous graph.
    transform = dgl.RowFeatNormalizer(subtract_min=True,
                                      node_feat_names=['h', 'h2'], edge_feat_names=['w'])
    g = dgl.heterograph({
        ('user', 'follows', 'user'): (F.tensor([1, 2]), F.tensor([3, 4])),
        ('player', 'plays', 'game'): (F.tensor([2, 2]), F.tensor([1, 1]))
    }, idtype=idtype, device=F.ctx())
    g.ndata['h'] = {'game': F.randn((2, 128)), 'player': F.randn((3, 128))}
    g.ndata['h2'] = {'user': F.randn((5, 128))}
    g.edata['w'] = {('user', 'follows', 'user'): F.randn((2, 128)), ('player', 'plays', 'game'): F.randn((2, 128))}
    g = transform(g)
    assert g.ndata['h']['game'].shape == (2, 128)
    assert g.ndata['h']['player'].shape == (3, 128)
    assert g.ndata['h2']['user'].shape == (5, 128)
    assert g.edata['w'][('user', 'follows', 'user')].shape == (2, 128)
    assert g.edata['w'][('player', 'plays', 'game')].shape == (2, 128)
    assert F.allclose(g.ndata['h']['game'].sum(1), F.tensor([1.0, 1.0]))
    assert F.allclose(g.ndata['h']['player'].sum(1), F.tensor([1.0, 1.0, 1.0]))
    assert F.allclose(g.ndata['h2']['user'].sum(1), F.tensor([1.0, 1.0, 1.0, 1.0, 1.0]))
    assert F.allclose(g.edata['w'][('user', 'follows', 'user')].sum(1), F.tensor([1.0, 1.0]))
    assert F.allclose(g.edata['w'][('player', 'plays', 'game')].sum(1), F.tensor([1.0, 1.0]))

@unittest.skipIf(dgl.backend.backend_name != 'pytorch', reason='Only support PyTorch for now')
@parametrize_idtype
def test_module_feat_mask(idtype):
    # Case1: Mask node and edge feature tensors of a homogeneous graph.
    transform = dgl.FeatMask(node_feat_names=['h'], edge_feat_names=['w'])
    g = dgl.rand_graph(5, 20, idtype=idtype, device=F.ctx())
    g.ndata['h'] = F.ones((g.num_nodes(), 10))
    g.edata['w'] = F.ones((g.num_edges(), 20))
    g = transform(g)
    assert g.device == g.device
    assert g.idtype == g.idtype
    assert g.ndata['h'].shape == (g.num_nodes(), 10)
    assert g.edata['w'].shape == (g.num_edges(), 20)

    # Case2: Mask node and edge feature tensors of a heterogeneous graph.
    g = dgl.heterograph({
        ('user', 'follows', 'user'): (F.tensor([1, 2]), F.tensor([3, 4])),
        ('player', 'plays', 'game'): (F.tensor([2, 2]), F.tensor([1, 1]))
    }, idtype=idtype, device=F.ctx())
    g.ndata['h'] = {'game': F.randn((2, 5)), 'player': F.randn((3, 5))}
    g.edata['w'] = {('user', 'follows', 'user'): F.randn((2, 5)),
                    ('player', 'plays', 'game'): F.randn((2, 5))}
    g = transform(g)
    assert g.device == g.device
    assert g.idtype == g.idtype
    assert g.ndata['h']['game'].shape == (2, 5)
    assert g.ndata['h']['player'].shape == (3, 5)
    assert g.edata['w'][('user', 'follows', 'user')].shape == (2, 5)
    assert g.edata['w'][('player', 'plays', 'game')].shape == (2, 5)

if __name__ == '__main__':
    test_partition_with_halo()
    test_module_heat_kernel(F.int32)