> what dose the input graph , shoud be undirected to make sense mean , in
> label propagation algorithm?
In my opinion, yes, it should be undirected because communities are not
well-defined for directed graphs anyway. (None of the classical, informal
definitions of a community take edge directions into account as far as I know).

> so what is the output when you run on a directed graph?
Labels will be propagated forward along the edges, but the convergence of the
algorithm is not guaranteed; for instance, nodes without inbound edges are free
to choose their labels in an arbitrary manner because no other nodes influence
them.

T.

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