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# 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.*

## Step 0: Problem description¶

We start with the well-known “Zachary’s karate club” problem. The karate club is a social network which captures 34 members and document 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¶

Creating the graph for Zachary’s karate club goes as follows:

```
import dgl
def build_karate_club_graph():
g = dgl.DGLGraph()
# add 34 nodes into the graph; nodes are labeled from 0~33
g.add_nodes(34)
# all 78 edges as a list of tuples
edge_list = [(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2),
(4, 0), (5, 0), (6, 0), (6, 4), (6, 5), (7, 0), (7, 1),
(7, 2), (7, 3), (8, 0), (8, 2), (9, 2), (10, 0), (10, 4),
(10, 5), (11, 0), (12, 0), (12, 3), (13, 0), (13, 1), (13, 2),
(13, 3), (16, 5), (16, 6), (17, 0), (17, 1), (19, 0), (19, 1),
(21, 0), (21, 1), (25, 23), (25, 24), (27, 2), (27, 23),
(27, 24), (28, 2), (29, 23), (29, 26), (30, 1), (30, 8),
(31, 0), (31, 24), (31, 25), (31, 28), (32, 2), (32, 8),
(32, 14), (32, 15), (32, 18), (32, 20), (32, 22), (32, 23),
(32, 29), (32, 30), (32, 31), (33, 8), (33, 9), (33, 13),
(33, 14), (33, 15), (33, 18), (33, 19), (33, 20), (33, 22),
(33, 23), (33, 26), (33, 27), (33, 28), (33, 29), (33, 30),
(33, 31), (33, 32)]
# add edges two lists of nodes: src and dst
src, dst = tuple(zip(*edge_list))
g.add_edges(src, dst)
# edges are directional in DGL; make them bi-directional
g.add_edges(dst, src)
return g
```

We can 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.
```

We can also 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
pos = nx.kamada_kawai_layout(nx_G)
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, we assign each node’s an input feature as a one-hot vector: node \(v_i\)‘s feature vector is \([0,\ldots,1,\dots,0]\), where the \(i^{th}\) position is one.

In DGL, we can add features for all nodes at once, using a feature tensor that batches node features along the first dimension. This code below adds the one-hot feature for all nodes:

```
import torch
G.ndata['feat'] = torch.eye(34)
```

We can print out the node features to verify:

```
# print out node 2's input feature
print(G.nodes[2].data['feat'])
# print out node 10 and 11's input features
print(G.nodes[[10, 11]].data['feat'])
```

Out:

```
tensor([[0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
tensor([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
```

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

To perform node classification, we use the Graph Convolutional Network (GCN) developed by Kipf and Welling. Here we provide the simplest definition of a GCN framework, but we recommend the reader to 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.

Now, we show that the GCN layer can be easily implemented in DGL.

```
import torch.nn as nn
import torch.nn.functional as F
# Define the message & reduce function
# NOTE: we ignore the GCN's normalization constant c_ij for this tutorial.
def gcn_message(edges):
# The argument is a batch of edges.
# This computes a (batch of) message called 'msg' using the source node's feature 'h'.
return {'msg' : edges.src['h']}
def gcn_reduce(nodes):
# The argument is a batch of nodes.
# This computes the new 'h' features by summing received 'msg' in each node's mailbox.
return {'h' : torch.sum(nodes.mailbox['msg'], dim=1)}
# Define the GCNLayer module
class GCNLayer(nn.Module):
def __init__(self, in_feats, out_feats):
super(GCNLayer, self).__init__()
self.linear = nn.Linear(in_feats, out_feats)
def forward(self, g, inputs):
# g is the graph and the inputs is the input node features
# first set the node features
g.ndata['h'] = inputs
# trigger message passing on all edges
g.send(g.edges(), gcn_message)
# trigger aggregation at all nodes
g.recv(g.nodes(), gcn_reduce)
# get the result node features
h = g.ndata.pop('h')
# perform linear transformation
return self.linear(h)
```

In general, the nodes send information computed via the *message functions*,
and aggregates incoming information with the *reduce functions*.

We then define a deeper GCN model that contains two GCN layers:

```
# Define a 2-layer GCN model
class GCN(nn.Module):
def __init__(self, in_feats, hidden_size, num_classes):
super(GCN, self).__init__()
self.gcn1 = GCNLayer(in_feats, hidden_size)
self.gcn2 = GCNLayer(hidden_size, num_classes)
def forward(self, g, inputs):
h = self.gcn1(g, inputs)
h = torch.relu(h)
h = self.gcn2(g, h)
return h
# The first layer transforms input features of size of 34 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(34, 5, 2)
```

## Step 4: data preparation and initialization¶

We use one-hot vectors 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 = torch.eye(34)
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.

```
optimizer = torch.optim.Adam(net.parameters(), lr=0.01)
all_logits = []
for epoch in range(30):
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)
optimizer.zero_grad()
loss.backward()
optimizer.step()
print('Epoch %d | Loss: %.4f' % (epoch, loss.item()))
```

Out:

```
Epoch 0 | Loss: 0.6606
Epoch 1 | Loss: 0.4522
Epoch 2 | Loss: 0.3218
Epoch 3 | Loss: 0.2363
Epoch 4 | Loss: 0.1765
Epoch 5 | Loss: 0.1290
Epoch 6 | Loss: 0.0923
Epoch 7 | Loss: 0.0666
Epoch 8 | Loss: 0.0466
Epoch 9 | Loss: 0.0318
Epoch 10 | Loss: 0.0210
Epoch 11 | Loss: 0.0137
Epoch 12 | Loss: 0.0090
Epoch 13 | Loss: 0.0060
Epoch 14 | Loss: 0.0041
Epoch 15 | Loss: 0.0029
Epoch 16 | Loss: 0.0021
Epoch 17 | Loss: 0.0016
Epoch 18 | Loss: 0.0012
Epoch 19 | Loss: 0.0010
Epoch 20 | Loss: 0.0008
Epoch 21 | Loss: 0.0006
Epoch 22 | Loss: 0.0005
Epoch 23 | Loss: 0.0004
Epoch 24 | Loss: 0.0004
Epoch 25 | Loss: 0.0003
Epoch 26 | Loss: 0.0003
Epoch 27 | Loss: 0.0003
Epoch 28 | Loss: 0.0002
Epoch 29 | Loss: 0.0002
```

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 0.401 seconds)