# DGL at a Glance¶

Author: Minjie Wang, Quan Gan, Jake Zhao, Zheng Zhang

DGL is a Python package dedicated to deep learning on graphs, built atop existing tensor DL frameworks (e.g. Pytorch, MXNet) and simplifying the implementation of graph-based neural networks.

The goal of this tutorial:

• Understand how DGL enables computation on graph from a high level.
• Train a simple graph neural network in DGL to classify nodes in a graph.

At the end of this tutorial, we hope you get a brief feeling of how DGL works.

This tutorial assumes basic familiarity with pytorch.

## Tutorial problem description¶

The tutorial is based on the “Zachary’s karate club” problem. The karate club is a social network that includes 34 members and documents pairwise links between members who interact outside the club. The club later divides into two communities led by the instructor (node 0) and the club president (node 33). The network is visualized as follows with the color indicating the community:

The task is to predict which side (0 or 33) each member tends to join given the social network itself.

## Step 1: Creating a graph in DGL¶

Create the graph for Zachary’s karate club as follows:

import dgl
import numpy as np

def build_karate_club_graph():
# All 78 edges are stored in two numpy arrays. One for source endpoints
# while the other for destination endpoints.
src = np.array([1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10, 10,
10, 11, 12, 12, 13, 13, 13, 13, 16, 16, 17, 17, 19, 19, 21, 21,
25, 25, 27, 27, 27, 28, 29, 29, 30, 30, 31, 31, 31, 31, 32, 32,
32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33,
33, 33, 33, 33, 33, 33, 33, 33, 33, 33])
dst = np.array([0, 0, 1, 0, 1, 2, 0, 0, 0, 4, 5, 0, 1, 2, 3, 0, 2, 2, 0, 4,
5, 0, 0, 3, 0, 1, 2, 3, 5, 6, 0, 1, 0, 1, 0, 1, 23, 24, 2, 23,
24, 2, 23, 26, 1, 8, 0, 24, 25, 28, 2, 8, 14, 15, 18, 20, 22, 23,
29, 30, 31, 8, 9, 13, 14, 15, 18, 19, 20, 22, 23, 26, 27, 28, 29, 30,
31, 32])
# Edges are directional in DGL; Make them bi-directional.
u = np.concatenate([src, dst])
v = np.concatenate([dst, src])
# Construct a DGLGraph
return dgl.DGLGraph((u, v))


Print out the number of nodes and edges in our newly constructed graph:

G = build_karate_club_graph()
print('We have %d nodes.' % G.number_of_nodes())
print('We have %d edges.' % G.number_of_edges())


Out:

We have 34 nodes.
We have 156 edges.


Visualize the graph by converting it to a networkx graph:

import networkx as nx
# Since the actual graph is undirected, we convert it for visualization
# purpose.
nx_G = G.to_networkx().to_undirected()
# Kamada-Kawaii layout usually looks pretty for arbitrary graphs
nx.draw(nx_G, pos, with_labels=True, node_color=[[.7, .7, .7]])


## Step 2: Assign features to nodes or edges¶

Graph neural networks associate features with nodes and edges for training. For our classification example, since there is no input feature, we assign each node with a learnable embedding vector.

# In DGL, you can add features for all nodes at once, using a feature tensor that
# batches node features along the first dimension. The code below adds the learnable
# embeddings for all nodes:

import torch
import torch.nn as nn
import torch.nn.functional as F

embed = nn.Embedding(34, 5)  # 34 nodes with embedding dim equal to 5
G.ndata['feat'] = embed.weight


Print out the node features to verify:

# print out node 2's input feature
print(G.ndata['feat'][2])

# print out node 10 and 11's input features
print(G.ndata['feat'][[10, 11]])


Out:

tensor([-2.4510, -0.6563, -0.7395,  1.6401,  2.2282], grad_fn=<SelectBackward>)
tensor([[-1.6371,  0.1195, -0.5801,  0.6771, -1.2104],
[-0.0391, -0.2906, -0.7418, -0.0126, -0.3276]],


## Step 3: Define a Graph Convolutional Network (GCN)¶

To perform node classification, use the Graph Convolutional Network (GCN) developed by Kipf and Welling. Here is the simplest definition of a GCN framework. We recommend that you read the original paper for more details.

• At layer $$l$$, each node $$v_i^l$$ carries a feature vector $$h_i^l$$.
• Each layer of the GCN tries to aggregate the features from $$u_i^{l}$$ where $$u_i$$‘s are neighborhood nodes to $$v$$ into the next layer representation at $$v_i^{l+1}$$. This is followed by an affine transformation with some non-linearity.

The above definition of GCN fits into a message-passing paradigm: Each node will update its own feature with information sent from neighboring nodes. A graphical demonstration is displayed below.

In DGL, we provide implementations of popular Graph Neural Network layers under the dgl.<backend>.nn subpackage. The GraphConv module implements one Graph Convolutional layer.

from dgl.nn.pytorch import GraphConv


Define a deeper GCN model that contains two GCN layers:

class GCN(nn.Module):
def __init__(self, in_feats, hidden_size, num_classes):
super(GCN, self).__init__()
self.conv1 = GraphConv(in_feats, hidden_size)
self.conv2 = GraphConv(hidden_size, num_classes)

def forward(self, g, inputs):
h = self.conv1(g, inputs)
h = torch.relu(h)
h = self.conv2(g, h)
return h

# The first layer transforms input features of size of 5 to a hidden size of 5.
# The second layer transforms the hidden layer and produces output features of
# size 2, corresponding to the two groups of the karate club.
net = GCN(5, 5, 2)


## Step 4: Data preparation and initialization¶

We use learnable embeddings to initialize the node features. Since this is a semi-supervised setting, only the instructor (node 0) and the club president (node 33) are assigned labels. The implementation is available as follow.

inputs = embed.weight
labeled_nodes = torch.tensor([0, 33])  # only the instructor and the president nodes are labeled
labels = torch.tensor([0, 1])  # their labels are different


## Step 5: Train then visualize¶

The training loop is exactly the same as other PyTorch models. We (1) create an optimizer, (2) feed the inputs to the model, (3) calculate the loss and (4) use autograd to optimize the model.

import itertools

all_logits = []
for epoch in range(50):
logits = net(G, inputs)
# we save the logits for visualization later
all_logits.append(logits.detach())
logp = F.log_softmax(logits, 1)
# we only compute loss for labeled nodes
loss = F.nll_loss(logp[labeled_nodes], labels)

loss.backward()
optimizer.step()

print('Epoch %d | Loss: %.4f' % (epoch, loss.item()))


Out:

Epoch 0 | Loss: 0.5709
Epoch 1 | Loss: 0.5381
Epoch 2 | Loss: 0.5062
Epoch 3 | Loss: 0.4742
Epoch 4 | Loss: 0.4429
Epoch 5 | Loss: 0.4122
Epoch 6 | Loss: 0.3817
Epoch 7 | Loss: 0.3518
Epoch 8 | Loss: 0.3218
Epoch 9 | Loss: 0.2928
Epoch 10 | Loss: 0.2650
Epoch 11 | Loss: 0.2386
Epoch 12 | Loss: 0.2138
Epoch 13 | Loss: 0.1909
Epoch 14 | Loss: 0.1696
Epoch 15 | Loss: 0.1502
Epoch 16 | Loss: 0.1324
Epoch 17 | Loss: 0.1163
Epoch 18 | Loss: 0.1019
Epoch 19 | Loss: 0.0892
Epoch 20 | Loss: 0.0780
Epoch 21 | Loss: 0.0681
Epoch 22 | Loss: 0.0595
Epoch 23 | Loss: 0.0520
Epoch 24 | Loss: 0.0455
Epoch 25 | Loss: 0.0399
Epoch 26 | Loss: 0.0350
Epoch 27 | Loss: 0.0308
Epoch 28 | Loss: 0.0272
Epoch 29 | Loss: 0.0241
Epoch 30 | Loss: 0.0214
Epoch 31 | Loss: 0.0190
Epoch 32 | Loss: 0.0170
Epoch 33 | Loss: 0.0153
Epoch 34 | Loss: 0.0137
Epoch 35 | Loss: 0.0124
Epoch 36 | Loss: 0.0112
Epoch 37 | Loss: 0.0102
Epoch 38 | Loss: 0.0094
Epoch 39 | Loss: 0.0086
Epoch 40 | Loss: 0.0079
Epoch 41 | Loss: 0.0073
Epoch 42 | Loss: 0.0068
Epoch 43 | Loss: 0.0063
Epoch 44 | Loss: 0.0059
Epoch 45 | Loss: 0.0055
Epoch 46 | Loss: 0.0052
Epoch 47 | Loss: 0.0049
Epoch 48 | Loss: 0.0046
Epoch 49 | Loss: 0.0044


This is a rather toy example, so it does not even have a validation or test set. Instead, Since the model produces an output feature of size 2 for each node, we can visualize by plotting the output feature in a 2D space. The following code animates the training process from initial guess (where the nodes are not classified correctly at all) to the end (where the nodes are linearly separable).

import matplotlib.animation as animation
import matplotlib.pyplot as plt

def draw(i):
cls1color = '#00FFFF'
cls2color = '#FF00FF'
pos = {}
colors = []
for v in range(34):
pos[v] = all_logits[i][v].numpy()
cls = pos[v].argmax()
colors.append(cls1color if cls else cls2color)
ax.cla()
ax.axis('off')
ax.set_title('Epoch: %d' % i)
nx.draw_networkx(nx_G.to_undirected(), pos, node_color=colors,
with_labels=True, node_size=300, ax=ax)

fig = plt.figure(dpi=150)
fig.clf()
ax = fig.subplots()
draw(0)  # draw the prediction of the first epoch
plt.close()


The following animation shows how the model correctly predicts the community after a series of training epochs.

ani = animation.FuncAnimation(fig, draw, frames=len(all_logits), interval=200)


## Next steps¶

In the next tutorial, we will go through some more basics of DGL, such as reading and writing node/edge features.

Total running time of the script: ( 0 minutes 0.565 seconds)

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