[graph-tool] Effect of hubs in WSBM

Tiago de Paula Peixoto tiago at skewed.de
Fri Jul 17 12:36:55 CEST 2020

Am 16.07.20 um 00:49 schrieb Dominik Schlechtweg:
> Hi Tiago,
> we noticed that with certain weighted graphs minimize_blockmodel_dl() tends to put hubs (vertices with many edges) into the same cluster. Please find a minimal example below, which produces the clustered graph in the attached plot. This happens even if edge weights are distributed uniformly over edges. Is this intended behavior?
> We wonder if a possible explanation could be that the WSBM is fit to predict edge weights *as well as edge probabilities*. (Compare to formulas (1) and (4) in [1].) Hence, vertices with similar degrees tend to end up in the same cluster, if the edge weights do not contradict this. Is this correct?

This has nothing to do with having weights or not; if you use an
unweighted SBM you get the same behavior.

This clustering makes sense under the model, because a random multigraph
model with the same degree sequence would yield a larger number of
connections between the hubs, and between the nodes with smaller degree.

See an explanation for this in this paper: https://arxiv.org/abs/2002.07803


Tiago de Paula Peixoto <tiago at skewed.de>

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