graph.cc

/*!
 *  Copyright (c) 2018 by Contributors
 * \file graph/graph.cc
 * \brief DGL graph index implementation
 */
#include <dgl/graph.h>
#include <algorithm>
#include <unordered_map>
#include <set>
#include <functional>
#include <tuple>
#include "../c_api_common.h"

namespace dgl {

Graph::Graph(IdArray src_ids, IdArray dst_ids, IdArray edge_ids, size_t num_nodes,
    bool multigraph): is_multigraph_(multigraph) {
  CHECK(IsValidIdArray(src_ids));
  CHECK(IsValidIdArray(dst_ids));
  CHECK(IsValidIdArray(edge_ids));
  this->AddVertices(num_nodes);
  num_edges_ = src_ids->shape[0];
  CHECK(static_cast<int64_t>(num_edges_) == dst_ids->shape[0])
    << "vectors in COO must have the same length";
  CHECK(static_cast<int64_t>(num_edges_) == edge_ids->shape[0])
    << "vectors in COO must have the same length";
  const dgl_id_t *src_data = static_cast<dgl_id_t*>(src_ids->data);
  const dgl_id_t *dst_data = static_cast<dgl_id_t*>(dst_ids->data);
  const dgl_id_t *edge_data = static_cast<dgl_id_t*>(edge_ids->data);
  all_edges_src_.reserve(num_edges_);
  all_edges_dst_.reserve(num_edges_);
  for (uint64_t i = 0; i < num_edges_; i++) {
    auto src = src_data[i];
    auto dst = dst_data[i];
    auto eid = edge_data[i];
    CHECK(HasVertex(src) && HasVertex(dst))
      << "Invalid vertices: src=" << src << " dst=" << dst;

    adjlist_[src].succ.push_back(dst);
    adjlist_[src].edge_id.push_back(eid);
    reverse_adjlist_[dst].succ.push_back(src);
    reverse_adjlist_[dst].edge_id.push_back(eid);

    all_edges_src_.push_back(src);
    all_edges_dst_.push_back(dst);
  }
}

void Graph::AddVertices(uint64_t num_vertices) {
  CHECK(!read_only_) << "Graph is read-only. Mutations are not allowed.";
  adjlist_.resize(adjlist_.size() + num_vertices);
  reverse_adjlist_.resize(reverse_adjlist_.size() + num_vertices);
}

void Graph::AddEdge(dgl_id_t src, dgl_id_t dst) {
  CHECK(!read_only_) << "Graph is read-only. Mutations are not allowed.";
  CHECK(HasVertex(src) && HasVertex(dst))
    << "Invalid vertices: src=" << src << " dst=" << dst;

  dgl_id_t eid = num_edges_++;

  adjlist_[src].succ.push_back(dst);
  adjlist_[src].edge_id.push_back(eid);
  reverse_adjlist_[dst].succ.push_back(src);
  reverse_adjlist_[dst].edge_id.push_back(eid);

  all_edges_src_.push_back(src);
  all_edges_dst_.push_back(dst);
}

void Graph::AddEdges(IdArray src_ids, IdArray dst_ids) {
  CHECK(!read_only_) << "Graph is read-only. Mutations are not allowed.";
  CHECK(IsValidIdArray(src_ids)) << "Invalid src id array.";
  CHECK(IsValidIdArray(dst_ids)) << "Invalid dst id array.";
  const auto srclen = src_ids->shape[0];
  const auto dstlen = dst_ids->shape[0];
  const int64_t* src_data = static_cast<int64_t*>(src_ids->data);
  const int64_t* dst_data = static_cast<int64_t*>(dst_ids->data);
  if (srclen == 1) {
    // one-many
    for (int64_t i = 0; i < dstlen; ++i) {
      AddEdge(src_data[0], dst_data[i]);
    }
  } else if (dstlen == 1) {
    // many-one
    for (int64_t i = 0; i < srclen; ++i) {
      AddEdge(src_data[i], dst_data[0]);
    }
  } else {
    // many-many
    CHECK(srclen == dstlen) << "Invalid src and dst id array.";
    for (int64_t i = 0; i < srclen; ++i) {
      AddEdge(src_data[i], dst_data[i]);
    }
  }
}

BoolArray Graph::HasVertices(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  BoolArray rst = BoolArray::Empty({len}, vids->dtype, vids->ctx);
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  int64_t* rst_data = static_cast<int64_t*>(rst->data);
  const int64_t nverts = NumVertices();
  for (int64_t i = 0; i < len; ++i) {
    rst_data[i] = (vid_data[i] < nverts)? 1 : 0;
  }
  return rst;
}

// O(E)
bool Graph::HasEdgeBetween(dgl_id_t src, dgl_id_t dst) const {
  if (!HasVertex(src) || !HasVertex(dst)) return false;
  const auto& succ = adjlist_[src].succ;
  return std::find(succ.begin(), succ.end(), dst) != succ.end();
}

// O(E*k) pretty slow
BoolArray Graph::HasEdgesBetween(IdArray src_ids, IdArray dst_ids) const {
  CHECK(IsValidIdArray(src_ids)) << "Invalid src id array.";
  CHECK(IsValidIdArray(dst_ids)) << "Invalid dst id array.";
  const auto srclen = src_ids->shape[0];
  const auto dstlen = dst_ids->shape[0];
  const auto rstlen = std::max(srclen, dstlen);
  BoolArray rst = BoolArray::Empty({rstlen}, src_ids->dtype, src_ids->ctx);
  int64_t* rst_data = static_cast<int64_t*>(rst->data);
  const int64_t* src_data = static_cast<int64_t*>(src_ids->data);
  const int64_t* dst_data = static_cast<int64_t*>(dst_ids->data);
  if (srclen == 1) {
    // one-many
    for (int64_t i = 0; i < dstlen; ++i) {
      rst_data[i] = HasEdgeBetween(src_data[0], dst_data[i])? 1 : 0;
    }
  } else if (dstlen == 1) {
    // many-one
    for (int64_t i = 0; i < srclen; ++i) {
      rst_data[i] = HasEdgeBetween(src_data[i], dst_data[0])? 1 : 0;
    }
  } else {
    // many-many
    CHECK(srclen == dstlen) << "Invalid src and dst id array.";
    for (int64_t i = 0; i < srclen; ++i) {
      rst_data[i] = HasEdgeBetween(src_data[i], dst_data[i])? 1 : 0;
    }
  }
  return rst;
}

// The data is copy-out; support zero-copy?
IdArray Graph::Predecessors(dgl_id_t vid, uint64_t radius) const {
  CHECK(HasVertex(vid)) << "invalid vertex: " << vid;
  CHECK(radius >= 1) << "invalid radius: " << radius;
  std::set<dgl_id_t> vset;

  for (auto& it : reverse_adjlist_[vid].succ)
    vset.insert(it);

  const int64_t len = vset.size();
  IdArray rst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  int64_t* rst_data = static_cast<int64_t*>(rst->data);

  std::copy(vset.begin(), vset.end(), rst_data);
  return rst;
}

// The data is copy-out; support zero-copy?
IdArray Graph::Successors(dgl_id_t vid, uint64_t radius) const {
  CHECK(HasVertex(vid)) << "invalid vertex: " << vid;
  CHECK(radius >= 1) << "invalid radius: " << radius;
  std::set<dgl_id_t> vset;

  for (auto& it : adjlist_[vid].succ)
    vset.insert(it);

  const int64_t len = vset.size();
  IdArray rst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  int64_t* rst_data = static_cast<int64_t*>(rst->data);

  std::copy(vset.begin(), vset.end(), rst_data);
  return rst;
}

// O(E)
IdArray Graph::EdgeId(dgl_id_t src, dgl_id_t dst) const {
  CHECK(HasVertex(src) && HasVertex(dst)) << "invalid edge: " << src << " -> " << dst;

  const auto& succ = adjlist_[src].succ;
  std::vector<dgl_id_t> edgelist;

  for (size_t i = 0; i < succ.size(); ++i) {
    if (succ[i] == dst)
      edgelist.push_back(adjlist_[src].edge_id[i]);
  }

  // FIXME: signed?  Also it seems that we are using int64_t everywhere...
  const int64_t len = edgelist.size();
  IdArray rst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  // FIXME: signed?
  int64_t* rst_data = static_cast<int64_t*>(rst->data);

  std::copy(edgelist.begin(), edgelist.end(), rst_data);

  return rst;
}

// O(E*k) pretty slow
Graph::EdgeArray Graph::EdgeIds(IdArray src_ids, IdArray dst_ids) const {
  CHECK(IsValidIdArray(src_ids)) << "Invalid src id array.";
  CHECK(IsValidIdArray(dst_ids)) << "Invalid dst id array.";
  const auto srclen = src_ids->shape[0];
  const auto dstlen = dst_ids->shape[0];
  int64_t i, j;

  CHECK((srclen == dstlen) || (srclen == 1) || (dstlen == 1))
    << "Invalid src and dst id array.";

  const int64_t src_stride = (srclen == 1 && dstlen != 1) ? 0 : 1;
  const int64_t dst_stride = (dstlen == 1 && srclen != 1) ? 0 : 1;
  const int64_t* src_data = static_cast<int64_t*>(src_ids->data);
  const int64_t* dst_data = static_cast<int64_t*>(dst_ids->data);

  std::vector<dgl_id_t> src, dst, eid;

  for (i = 0, j = 0; i < srclen && j < dstlen; i += src_stride, j += dst_stride) {
    const dgl_id_t src_id = src_data[i], dst_id = dst_data[j];
    CHECK(HasVertex(src_id) && HasVertex(dst_id)) <<
        "invalid edge: " << src_id << " -> " << dst_id;
    const auto& succ = adjlist_[src_id].succ;
    for (size_t k = 0; k < succ.size(); ++k) {
      if (succ[k] == dst_id) {
        src.push_back(src_id);
        dst.push_back(dst_id);
        eid.push_back(adjlist_[src_id].edge_id[k]);
      }
    }
  }

  int64_t rstlen = src.size();
  IdArray rst_src = IdArray::Empty({rstlen}, src_ids->dtype, src_ids->ctx);
  IdArray rst_dst = IdArray::Empty({rstlen}, src_ids->dtype, src_ids->ctx);
  IdArray rst_eid = IdArray::Empty({rstlen}, src_ids->dtype, src_ids->ctx);
  int64_t* rst_src_data = static_cast<int64_t*>(rst_src->data);
  int64_t* rst_dst_data = static_cast<int64_t*>(rst_dst->data);
  int64_t* rst_eid_data = static_cast<int64_t*>(rst_eid->data);

  std::copy(src.begin(), src.end(), rst_src_data);
  std::copy(dst.begin(), dst.end(), rst_dst_data);
  std::copy(eid.begin(), eid.end(), rst_eid_data);

  return EdgeArray{rst_src, rst_dst, rst_eid};
}

Graph::EdgeArray Graph::FindEdges(IdArray eids) const {
  int64_t len = eids->shape[0];

  IdArray rst_src = IdArray::Empty({len}, eids->dtype, eids->ctx);
  IdArray rst_dst = IdArray::Empty({len}, eids->dtype, eids->ctx);
  IdArray rst_eid = IdArray::Empty({len}, eids->dtype, eids->ctx);
  int64_t* eid_data = static_cast<int64_t*>(eids->data);
  int64_t* rst_src_data = static_cast<int64_t*>(rst_src->data);
  int64_t* rst_dst_data = static_cast<int64_t*>(rst_dst->data);
  int64_t* rst_eid_data = static_cast<int64_t*>(rst_eid->data);

  for (uint64_t i = 0; i < (uint64_t)len; ++i) {
    dgl_id_t eid = eid_data[i];
    if (eid >= num_edges_)
      LOG(FATAL) << "invalid edge id:" << eid;

    rst_src_data[i] = all_edges_src_[eid];
    rst_dst_data[i] = all_edges_dst_[eid];
    rst_eid_data[i] = eid;
  }

  return EdgeArray{rst_src, rst_dst, rst_eid};
}

// O(E)
Graph::EdgeArray Graph::InEdges(dgl_id_t vid) const {
  CHECK(HasVertex(vid)) << "invalid vertex: " << vid;
  const int64_t len = reverse_adjlist_[vid].succ.size();
  IdArray src = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray dst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray eid = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  int64_t* src_data = static_cast<int64_t*>(src->data);
  int64_t* dst_data = static_cast<int64_t*>(dst->data);
  int64_t* eid_data = static_cast<int64_t*>(eid->data);
  for (int64_t i = 0; i < len; ++i) {
    src_data[i] = reverse_adjlist_[vid].succ[i];
    eid_data[i] = reverse_adjlist_[vid].edge_id[i];
  }
  std::fill(dst_data, dst_data + len, vid);
  return EdgeArray{src, dst, eid};
}

// O(E)
Graph::EdgeArray Graph::InEdges(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  int64_t rstlen = 0;
  for (int64_t i = 0; i < len; ++i) {
    CHECK(HasVertex(vid_data[i])) << "Invalid vertex: " << vid_data[i];
    rstlen += reverse_adjlist_[vid_data[i]].succ.size();
  }
  IdArray src = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  IdArray dst = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  IdArray eid = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  int64_t* src_ptr = static_cast<int64_t*>(src->data);
  int64_t* dst_ptr = static_cast<int64_t*>(dst->data);
  int64_t* eid_ptr = static_cast<int64_t*>(eid->data);
  for (int64_t i = 0; i < len; ++i) {
    const auto& pred = reverse_adjlist_[vid_data[i]].succ;
    const auto& eids = reverse_adjlist_[vid_data[i]].edge_id;
    for (size_t j = 0; j < pred.size(); ++j) {
      *(src_ptr++) = pred[j];
      *(dst_ptr++) = vid_data[i];
      *(eid_ptr++) = eids[j];
    }
  }
  return EdgeArray{src, dst, eid};
}

// O(E)
Graph::EdgeArray Graph::OutEdges(dgl_id_t vid) const {
  CHECK(HasVertex(vid)) << "invalid vertex: " << vid;
  const int64_t len = adjlist_[vid].succ.size();
  IdArray src = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray dst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray eid = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  int64_t* src_data = static_cast<int64_t*>(src->data);
  int64_t* dst_data = static_cast<int64_t*>(dst->data);
  int64_t* eid_data = static_cast<int64_t*>(eid->data);
  for (int64_t i = 0; i < len; ++i) {
    dst_data[i] = adjlist_[vid].succ[i];
    eid_data[i] = adjlist_[vid].edge_id[i];
  }
  std::fill(src_data, src_data + len, vid);
  return EdgeArray{src, dst, eid};
}

// O(E)
Graph::EdgeArray Graph::OutEdges(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  int64_t rstlen = 0;
  for (int64_t i = 0; i < len; ++i) {
    CHECK(HasVertex(vid_data[i])) << "Invalid vertex: " << vid_data[i];
    rstlen += adjlist_[vid_data[i]].succ.size();
  }
  IdArray src = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  IdArray dst = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  IdArray eid = IdArray::Empty({rstlen}, vids->dtype, vids->ctx);
  int64_t* src_ptr = static_cast<int64_t*>(src->data);
  int64_t* dst_ptr = static_cast<int64_t*>(dst->data);
  int64_t* eid_ptr = static_cast<int64_t*>(eid->data);
  for (int64_t i = 0; i < len; ++i) {
    const auto& succ = adjlist_[vid_data[i]].succ;
    const auto& eids = adjlist_[vid_data[i]].edge_id;
    for (size_t j = 0; j < succ.size(); ++j) {
      *(src_ptr++) = vid_data[i];
      *(dst_ptr++) = succ[j];
      *(eid_ptr++) = eids[j];
    }
  }
  return EdgeArray{src, dst, eid};
}

// O(E*log(E)) if sort is required; otherwise, O(E)
Graph::EdgeArray Graph::Edges(const std::string &order) const {
  const int64_t len = num_edges_;
  IdArray src = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray dst = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});
  IdArray eid = IdArray::Empty({len}, DLDataType{kDLInt, 64, 1}, DLContext{kDLCPU, 0});

  if (order == "srcdst") {
    typedef std::tuple<int64_t, int64_t, int64_t> Tuple;
    std::vector<Tuple> tuples;
    tuples.reserve(len);
    for (uint64_t eid = 0; eid < num_edges_; ++eid) {
      tuples.emplace_back(all_edges_src_[eid], all_edges_dst_[eid], eid);
    }
    // sort according to src and dst ids
    std::sort(tuples.begin(), tuples.end(),
        [] (const Tuple& t1, const Tuple& t2) {
          return std::get<0>(t1) < std::get<0>(t2)
            || (std::get<0>(t1) == std::get<0>(t2) && std::get<1>(t1) < std::get<1>(t2));
        });

    // make return arrays
    int64_t* src_ptr = static_cast<int64_t*>(src->data);
    int64_t* dst_ptr = static_cast<int64_t*>(dst->data);
    int64_t* eid_ptr = static_cast<int64_t*>(eid->data);
    for (size_t i = 0; i < tuples.size(); ++i) {
      src_ptr[i] = std::get<0>(tuples[i]);
      dst_ptr[i] = std::get<1>(tuples[i]);
      eid_ptr[i] = std::get<2>(tuples[i]);
    }
  } else {
    int64_t* src_ptr = static_cast<int64_t*>(src->data);
    int64_t* dst_ptr = static_cast<int64_t*>(dst->data);
    int64_t* eid_ptr = static_cast<int64_t*>(eid->data);
    std::copy(all_edges_src_.begin(), all_edges_src_.end(), src_ptr);
    std::copy(all_edges_dst_.begin(), all_edges_dst_.end(), dst_ptr);
    for (uint64_t eid = 0; eid < num_edges_; ++eid) {
      eid_ptr[eid] = eid;
    }
  }

  return EdgeArray{src, dst, eid};
}

// O(V)
DegreeArray Graph::InDegrees(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  DegreeArray rst = DegreeArray::Empty({len}, vids->dtype, vids->ctx);
  int64_t* rst_data = static_cast<int64_t*>(rst->data);
  for (int64_t i = 0; i < len; ++i) {
    const auto vid = vid_data[i];
    CHECK(HasVertex(vid)) << "Invalid vertex: " << vid;
    rst_data[i] = reverse_adjlist_[vid].succ.size();
  }
  return rst;
}

// O(V)
DegreeArray Graph::OutDegrees(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  DegreeArray rst = DegreeArray::Empty({len}, vids->dtype, vids->ctx);
  int64_t* rst_data = static_cast<int64_t*>(rst->data);
  for (int64_t i = 0; i < len; ++i) {
    const auto vid = vid_data[i];
    CHECK(HasVertex(vid)) << "Invalid vertex: " << vid;
    rst_data[i] = adjlist_[vid].succ.size();
  }
  return rst;
}

Subgraph Graph::VertexSubgraph(IdArray vids) const {
  CHECK(IsValidIdArray(vids)) << "Invalid vertex id array.";
  const auto len = vids->shape[0];
  std::unordered_map<dgl_id_t, dgl_id_t> oldv2newv;
  std::vector<dgl_id_t> edges;
  const int64_t* vid_data = static_cast<int64_t*>(vids->data);
  for (int64_t i = 0; i < len; ++i) {
    oldv2newv[vid_data[i]] = i;
  }
  Subgraph rst;
  rst.graph = std::make_shared<Graph>(IsMultigraph());
  rst.induced_vertices = vids;
  rst.graph->AddVertices(len);
  for (int64_t i = 0; i < len; ++i) {
    const dgl_id_t oldvid = vid_data[i];
    const dgl_id_t newvid = i;
    for (size_t j = 0; j < adjlist_[oldvid].succ.size(); ++j) {
      const dgl_id_t oldsucc = adjlist_[oldvid].succ[j];
      if (oldv2newv.count(oldsucc)) {
        const dgl_id_t newsucc = oldv2newv[oldsucc];
        edges.push_back(adjlist_[oldvid].edge_id[j]);
        rst.graph->AddEdge(newvid, newsucc);
      }
    }
  }
  rst.induced_edges = IdArray::Empty({static_cast<int64_t>(edges.size())}, vids->dtype, vids->ctx);
  std::copy(edges.begin(), edges.end(), static_cast<int64_t*>(rst.induced_edges->data));
  return rst;
}

Subgraph Graph::EdgeSubgraph(IdArray eids) const {
  CHECK(IsValidIdArray(eids)) << "Invalid vertex id array.";

  const auto len = eids->shape[0];
  std::unordered_map<dgl_id_t, dgl_id_t> oldv2newv;
  std::vector<dgl_id_t> nodes;
  const int64_t* eid_data = static_cast<int64_t*>(eids->data);

  for (int64_t i = 0; i < len; ++i) {
    dgl_id_t src_id = all_edges_src_[eid_data[i]];
    dgl_id_t dst_id = all_edges_dst_[eid_data[i]];
    if (oldv2newv.insert(std::make_pair(src_id, oldv2newv.size())).second)
      nodes.push_back(src_id);
    if (oldv2newv.insert(std::make_pair(dst_id, oldv2newv.size())).second)
      nodes.push_back(dst_id);
  }

  Subgraph rst;
  rst.graph = std::make_shared<Graph>(IsMultigraph());
  rst.induced_edges = eids;
  rst.graph->AddVertices(nodes.size());

  for (int64_t i = 0; i < len; ++i) {
    dgl_id_t src_id = all_edges_src_[eid_data[i]];
    dgl_id_t dst_id = all_edges_dst_[eid_data[i]];
    rst.graph->AddEdge(oldv2newv[src_id], oldv2newv[dst_id]);
  }

  rst.induced_vertices = IdArray::Empty(
      {static_cast<int64_t>(nodes.size())}, eids->dtype, eids->ctx);
  std::copy(nodes.begin(), nodes.end(), static_cast<int64_t*>(rst.induced_vertices->data));

  return rst;
}

std::vector<IdArray> Graph::GetAdj(bool transpose, const std::string &fmt) const {
  uint64_t num_edges = NumEdges();
  uint64_t num_nodes = NumVertices();
  if (fmt == "coo") {
    IdArray idx = IdArray::Empty(
        {2 * static_cast<int64_t>(num_edges)},
        DLDataType{kDLInt, 64, 1},
        DLContext{kDLCPU, 0});
    int64_t *idx_data = static_cast<int64_t*>(idx->data);
    if (transpose) {
      std::copy(all_edges_src_.begin(), all_edges_src_.end(), idx_data);
      std::copy(all_edges_dst_.begin(), all_edges_dst_.end(), idx_data + num_edges);
    } else {
      std::copy(all_edges_dst_.begin(), all_edges_dst_.end(), idx_data);
      std::copy(all_edges_src_.begin(), all_edges_src_.end(), idx_data + num_edges);
    }
    IdArray eid = IdArray::Empty(
        {static_cast<int64_t>(num_edges)},
        DLDataType{kDLInt, 64, 1},
        DLContext{kDLCPU, 0});
    int64_t *eid_data = static_cast<int64_t*>(eid->data);
    for (uint64_t eid = 0; eid < num_edges; ++eid) {
      eid_data[eid] = eid;
    }
    return std::vector<IdArray>{idx, eid};
  } else if (fmt == "csr") {
    IdArray indptr = IdArray::Empty(
        {static_cast<int64_t>(num_nodes) + 1},
        DLDataType{kDLInt, 64, 1},
        DLContext{kDLCPU, 0});
    IdArray indices = IdArray::Empty(
        {static_cast<int64_t>(num_edges)},
        DLDataType{kDLInt, 64, 1},
        DLContext{kDLCPU, 0});
    IdArray eid = IdArray::Empty(
        {static_cast<int64_t>(num_edges)},
        DLDataType{kDLInt, 64, 1},
        DLContext{kDLCPU, 0});
    int64_t *indptr_data = static_cast<int64_t*>(indptr->data);
    int64_t *indices_data = static_cast<int64_t*>(indices->data);
    int64_t *eid_data = static_cast<int64_t*>(eid->data);
    const AdjacencyList *adjlist;
    if (transpose) {
      // Out-edges.
      adjlist = &adjlist_;
    } else {
      // In-edges.
      adjlist = &reverse_adjlist_;
    }
    indptr_data[0] = 0;
    for (size_t i = 0; i < adjlist->size(); i++) {
      indptr_data[i + 1] = indptr_data[i] + adjlist->at(i).succ.size();
      std::copy(adjlist->at(i).succ.begin(), adjlist->at(i).succ.end(),
                indices_data + indptr_data[i]);
      std::copy(adjlist->at(i).edge_id.begin(), adjlist->at(i).edge_id.end(),
                eid_data + indptr_data[i]);
    }
    return std::vector<IdArray>{indptr, indices, eid};
  } else {
    LOG(FATAL) << "unsupported format";
    return std::vector<IdArray>();
  }
}

GraphPtr Graph::Reverse() const {
  LOG(FATAL) << "not implemented";
  return nullptr;
}

}  // namespace dgl