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 <ti...@skewed.de>
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