thanks, short follow-up: Am 17.07.20 um 12:36 schrieb Tiago de Paula Peixoto: > 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.
I see that we are probably mixing up two things here. Regarding this point: > is there a way to suppress the likelihood of the edge probabilities as in [2] > where the alpha-parameter can be used to fit "only to the weight > information"? (Compare to formula (4) in [2].) > [...] > [2] C. Aicher, A. Z. Jacobs, and A. Clauset. 2014. Learning latent block > structure in weighted networks. Journal of Complex Networks, 3(2):221–248. How does the graph-tools implementation relate to the alpha-parameter in formula (4)? Is it equivalent to giving equal weight to edge probabilities and weights (alpha = 0.5)? > > 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 Is it possible to use LatentMultigraphBlockState() with a weighted graph? > > Best, > Tiago > > > > _______________________________________________ > graph-tool mailing list > [email protected] > https://lists.skewed.de/mailman/listinfo/graph-tool >
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