[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

Best,
Tiago


-- 
Tiago de Paula Peixoto <tiago at skewed.de>

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