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
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