Discrepancy between "contains_isolated_nodes" and "edge_index_undirected"

[FeynmanDNA]

Strangely even though print(f'Contains isolated nodes: {data.contains_isolated_nodes()}') returns True, the networkx converted graph reports no sub-graphs: nx.number_connected_components(G) == 1

Then I looked into the difference between edge_index and edge_index_undirected and noticed some discrepancy.

Python code to reproduce my observation:

selected_dataset = 'synthetic_graph_1'
splitting_strategy = 'random'

dataset = LinkVesselGraph(
    root='data', 
    name=selected_dataset,
    splitting_strategy=splitting_strategy,
    use_edge_attr=True,
    use_atlas=True,
)

data = dataset[0]  # Get the first graph object.
print(data)

# Gather some statistics about the graph.
print(f'Number of nodes in graph: {data.num_nodes}')
print(f'Number of edges in graph: {data.num_edges}')
print(f'Average node degree: {data.num_edges / data.num_nodes:.2f}')
print(f'Contains isolated nodes: {data.contains_isolated_nodes()}')
print(f'Contains self-loops: {data.contains_self_loops()}')
print(f'Is Undirected: {data.is_undirected()}')

print(f'Number of undirected edges', data.edge_index_undirected.size(dim=1))
print(f'Number of training edges', data.train_pos_edge_index.size(dim=1))
print(f'Number of validation edges', data.val_pos_edge_index.size(dim=1))
print(f'Number of test edges', data.test_pos_edge_index.size(dim=1))

print(data.edge_index[:, 10:20])
"""
tensor([[  10,   11,   12,   13,   15,   17,   19,   20,   21,   22],
        [1642, 1679, 1658, 1553, 1559, 1564, 1593, 1656, 1565, 1549]])
"""

print(data.edge_index_undirected[:, 26:36])
"""
tensor([[  13, 1553,   14, 1629,   15, 1559,   16, 1580,   17, 1564],
        [1553,   13, 1629,   14, 1559,   15, 1580,   16, 1564,   17]])
"""

Note that edge_index reports no edge for node 14 and 16, but edge_index_undirected somehow returns edges that involves node 14 and 16

In fact, after the networkx conversion, if like data.contains_isolated_nodes() said, it has isolated nodes, then we should see subgraphs of connected components, but strangely we get a singe graph:

data_undirected = Data(x=data.x, edge_index = data.edge_index_undirected,
                    edge_attr = data.edge_attr_undirected)

G = to_networkx(
    data_undirected,
    to_undirected=True,  # to undirected for is_connected()
)
print("Networkx: #nodes, #edges", G.number_of_nodes(), G.number_of_edges())

# G connected?
print(f"nx.is_connected(G): {nx.is_connected(G)}")
print(f"nx.number_connected_components(G): {nx.number_connected_components(G)}")
"""
Networkx: #nodes, #edges 3197 3249
nx.is_connected(G): True
nx.number_connected_components(G): 1
"""

I tried remove_isolated_nodes and it reports similar observations.

Looks like edge_index_undirected is custom-made, maybe there is some logic that connects isolated nodes somehow that users should be be aware of?

Thanks!

[FeynmanDNA]

Hmm, I just realized I was confused by the edge_index's relationship to training set again... which @jqmcginnis you have already kindly explained here (https://github.com/jocpae/VesselGraph/issues/12#issuecomment-1148524602)

So it is not surprising that the training set contains isolated nodes (like node 14 and 16 in the above example), since they are randomly chosen to be part of training or not.

[jqmcginnis]

@FeynmanDNA sorry once again for the late response!

Thank you very much for the observation! Do you see any intuitive way of handling this to a better extent? I am still not very happy with the terminology of edge_index, edge_index_undirected and the training, validation and test masks. Do you see anyway of handling this in a better way, or should we stick to it for now?

[FeynmanDNA]

@jqmcginnis like you mentioned in your code comment that the link dataset adheres to the convention that only training edges are present in the data.edge_index. I recommend sticking to the community convention :)