build symmetric adjacency matrix

[laoreja]

Hi tkipf, thank you for your amazing work!
in utils.py, starts from Line 36,

    # build symmetric adjacency matrix
    adj = adj + adj.T.multiply(adj.T > adj) - adj.multiply(adj.T > adj)

As far as I understand, these lines are turning a directed adjacency matrix into an undirected adjacency matrix?
Since adj is a 0-1 matrix, then for the positions adj[i,j] where adj.T > adj, we should have adj[i,j] = 0, so the - adj.multiply(adj.T > adj) part is always zero.

Then what's the purpose of having that part, or am I understand it incorrectly?

[tkipf]

Yes, for binary adjacency matrices you are right. In all other cases you need the last term to ensure that only a single edge is kept (the one with largest weight).

[fansariadeh]

I do not understand why adj matrix should be turned into a symmetric matrix. Could you please clarify it?

[baojianzhou]

@fansariadeh. Based on my understanding, the original GCN paper considers undirected graphs. In some datasets, the graph may not be undirected ( e.g. store as the directed graph). This line of code can make sure the input graph be undirected.

[fansariadeh]

@fansariadeh. Based on my understanding, the original GCN paper considers undirected graphs. In some datasets, the graph may not be undirected ( e.g. store as the directed graph). This line of code can make sure the input graph be undirected.

Dear @baojianzhou
That makes sense to me now. I appreciate it.
Cheers,