 Hi,

I am trying to understand the output of and how it works.
I was going over previous question:

What I currently don’t understand in the above example, is:

1. Why does pos_graph have 4 nodes and 1 edge only?
2. What is the relationship between block to pos and neg graphs? Why do block have more nodes?

Thanks!

`pos_graph`, `neg_graph`, and the last block’s output nodes are the same. They represent all the nodes whose output representations from the GNN are involved in computing the scores of positive and negative examples. The blocks have more nodes so that you can perform message passing block by block, then put the output representations on the nodes in `pos_graph` and `neg_graph`, and use `apply_edges` to compute the positive and negative example scores.

Sorry but I still dont get it though. I’ve simplified the Graph in the above example to be:

Can you please explain what do you mean by “last block” here? As seen below, each step here has just 1 block.

``````# edges to compute output
train_eids = th.tensor([0, 1])
print(print("edges to compute output, src, dst are: ", G.find_edges(train_eids)))

fanouts =   # List of neighbors to sample for each GNN layer, let's say just one layer and one neighbor.

negative_sampler = NegativeSampler(G, 2)  # 2 negative samples per positive

G,
train_eids,
sampler,
exclude=None,
negative_sampler=negative_sampler,
batch_size=1,
shuffle=True,
drop_last=False,
pin_memory=True)
``````

``````   for step, (input_nodes, pos_graph, neg_graph, blocks) in enumerate(dataloader):
assert sum(th.eq(pos_graph.nodes(), neg_graph.nodes())) == \
neg_graph.number_of_nodes() == \
pos_graph.number_of_nodes()
print("************ step-{} **********".format(step))
print("input_nodes: ", input_nodes)
print("pos_graph {} edges: ".format(pos_graph.number_of_edges()), pos_graph.edges())
print("pos_graph {} nodes: ".format(pos_graph.number_of_nodes()), pos_graph.nodes())
print("pos_graph {} original edges: ".format(pos_graph.number_of_edges()), pos_graph.edata[dgl.EID])
print("pos_graph {} original nodes: ".format(pos_graph.number_of_nodes()), pos_graph.ndata[dgl.NID])
# neg_graph edges number == number defined in NegativeSampler()
print("neg_graph {} edges: ".format(neg_graph.number_of_edges()), neg_graph.edges())
print("neg_graph {} nodes: ".format(neg_graph.number_of_nodes()), neg_graph.nodes())
for b in blocks:
print("\tblock nodes number: ", b.number_of_nodes())
print("\tblock nodes: ", b.nodes("_U"))
print("\tblock edges: ", b.edges("uv"))
``````

And get this output:

``````************ step-0 **********
input_nodes:  tensor([1, 0, 5, 4])
pos_graph 1 edges:  (tensor(), tensor())
pos_graph 3 nodes:  tensor([0, 1, 2])
pos_graph 1 original edges:  tensor()
pos_graph 3 original nodes:  tensor([1, 0, 5])
neg_graph 2 edges:  (tensor([0, 0]), tensor([1, 2]))
neg_graph 3 nodes:  tensor([0, 1, 2])
block nodes number:  7
block nodes:  tensor([0, 1, 2, 3])
block edges:  (tensor([1, 3, 3]), tensor([0, 1, 2]))
************ step-1 **********
input_nodes:  tensor([2, 3, 5, 1, 4, 0])
pos_graph 1 edges:  (tensor(), tensor())
pos_graph 4 nodes:  tensor([0, 1, 2, 3])
pos_graph 1 original edges:  tensor()
pos_graph 4 original nodes:  tensor([2, 3, 5, 1])
neg_graph 2 edges:  (tensor([0, 0]), tensor([2, 3]))
neg_graph 4 nodes:  tensor([0, 1, 2, 3])
block nodes number:  10
block nodes:  tensor([0, 1, 2, 3, 4, 5])
block edges:  (tensor([1, 3, 4, 5]), tensor([0, 1, 2, 3]))
``````

Looking at the first step -
It seems the edges in the block do not correlate to either pos or neg graph. Why is that?

The graphs and blocks returned by `NodeDataLoader` and `EdgeDataLoader` are relabeled. The original node and edge IDs are stored as node feature `dgl.NID` and edge feature `dgl.EID`.

So if you want to see the original IDs of the edges and nodes sampled in `neg_graph` and `blocks` you will need to do the following:

``````neg_graph_nid = neg_graph.ndata[dgl.NID]
neg_graph_src, neg_graph_dst = neg_graph.edges()
neg_graph_src = neg_graph.ndata[dgl.NID][neg_graph_src]
neg_graph_dst = neg_graph.ndata[dgl.NID][neg_graph_dst]

# Input nodes of a block
block.srcdata[dgl.NID]
# Output nodes of a block
block.dstdata[dgl.NID]
# Edges of a block
block.edata[dgl.EID]
``````

The sampled nodes of the positive graph, the negative graph, and the output nodes of the block for the last GNN layer (i.e. `blocks[-1]`) are the same.

``````print(pos_graph.ndata[dgl.NID])
print(neg_graph.ndata[dgl.NID])
print(blocks[-1].dstdata[dgl.NID])
``````

These nodes are essentially the union of incident nodes of the sampled edges in the minibatch and the sampled negative pairs.