[graph-tool] Effect of hubs in WSBM

Dominik Schlechtweg dominik.schlechtweg at gmx.de
Fri Jul 17 20:35:38 CEST 2020

Am 17.07.20 um 19:44 schrieb Tiago de Paula Peixoto:
> Am 17.07.20 um 14:19 schrieb Dominik Schlechtweg:
>>> 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 parameter is not implemented in graph-tool.
> Note that such a parameter does not have an obvious interpretation from
> a generative modelling point of view, specially in a Bayesian way. We
> cannot just introduce ad-hoc parameters to cancel certain parts of the
> likelihood, without paying proper attention to issues of normalization,
> etc, and expect things to behave consistently.
> In other words, I do not fully agree with the alpha parameter of Aicher
> et al.

Thanks for clarifying this. Last question: Does your doubt also concern the special case where alpha = 0, i.e., ignoring edge probabilities completely? (This is the actually interesting case for us. We are not interested in tuning this parameter in any way.)

>> Is it possible to use LatentMultigraphBlockState() with a weighted graph?
> Not yet.

We will open a feature request then, in case there is none yet.

> Best,
> Tiago
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