dear graph-tool mailing list,

do you have any recommendations for modelling highly skewed distributions of

discrete edge weights?

my network is a multigraph which i collapse to a simple graph with

edge-weights represent the number of edges in the multigraph between two

vertices

in my data, the modal edge weight is equal to 1, but the max is above 2000

if i fit a degree-corrected Poisson SBM to the multigraph, every pair of

firms with a large number of edges together are grouped together in their

own block. this makes sense, since the poisson model will assign very low

probability to the edges for any value of a poisson parameter that can

rationalize the otherwise sparse rate of edge formation.

while this is not necessarily a problem per se, the large number of blocks

that this creates complicates my analysis considerably, and it would be

useful to use edge-covariates with a distribution that can account for the

skewness to get a smaller number of blocks.

wondering if Tiago or anyone else on the list can suggest any

transformation-distribution combination that might help. i tried (without

thinking too deeply) the transformation weight = log(weight) + 1 with

real-geometric weights, but minimize_blockmodel_dl() was taking an unusually

long time to fit so i escaped.

the other option that came to my mind was to use a hierarchical SBM and

choose a higher level where the blocks are merged. i haven't read the papers

on hierarchical SBM or used them in graph-tool yet.

thx,

-sam

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