Fix tutorial (#1587)

tutorials/models/1_gnn/1_gcn.py

@@ -126,6 +126,8 @@ def evaluate(model, g, features, labels, mask):
 import time
 import numpy as np
 g, features, labels, train_mask, test_mask = load_cora_data()
+# Add edges between each node and itself to preserve old node representations
+g.add_edges(g.nodes(), g.nodes())
 optimizer = th.optim.Adam(net.parameters(), lr=1e-2)
 dur = []
 for epoch in range(50):
@@ -159,14 +161,14 @@ for epoch in range(50):
 # 
 # Here, :math:`H^{(l)}` denotes the :math:`l^{th}` layer in the network,
 # :math:`\sigma` is the non-linearity, and :math:`W` is the weight matrix for
-# this layer. :math:`D` and :math:`A`, as commonly seen, represent degree
-# matrix and adjacency matrix, respectively. The ~ is a renormalization trick
-# in which we add a self-connection to each node of the graph, and build the
-# corresponding degree and adjacency matrix.  The shape of the input
+# this layer. :math:`\tilde{D}` and :math:`\tilde{A}` are separately the degree
+# and adjacency matrices for the graph. With the superscript ~, we are referring
+# to the variant where we add additional edges between each node and itself to
+# preserve its old representation in graph convolutions. The shape of the input
 # :math:`H^{(0)}` is :math:`N \times D`, where :math:`N` is the number of nodes
 # and :math:`D` is the number of input features. We can chain up multiple
 # layers as such to produce a node-level representation output with shape
-# :math`N \times F`, where :math:`F` is the dimension of the output node
+# :math:`N \times F`, where :math:`F` is the dimension of the output node
 # feature vector.
 #
 # The equation can be efficiently implemented using sparse matrix
@@ -174,3 +176,8 @@ for epoch in range(50):
 # `pygcn <https://github.com/tkipf/pygcn>`_ code). The above DGL implementation
 # in fact has already used this trick due to the use of builtin functions. To
 # understand what is under the hood, please read our tutorial on :doc:`PageRank <../../basics/3_pagerank>`.
+#
+# Note that the tutorial code implements a simplified version of GCN where we
+# replace :math:`\tilde{D}^{-\frac{1}{2}}\tilde{A}\tilde{D}^{-\frac{1}{2}}` with
+# :math:`\tilde{A}`. For a full implementation, see our example
+# `here  <https://github.com/dmlc/dgl/tree/master/examples/pytorch/gcn>`_.