edge multiplicities vs edge covariates

As I understand, edge multiplicities is kind of number of edges between two
And we can define it via 'eweight' attribute in BlockState. In some way
(may be I'm wrong)
if I differentiate initial edges by assigning to them different 'weights'
via 'eweight', I
will have also weighted graph model.
What is the difference between edge covariates and edge multiplicities
besides the generative model priors? Or I can consider them as a special
simple case
of more general 'edge covariates' of 'recs' attribute?
Is there any discussion about this?

Thank you.

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If you specify the "eweight" parameter, you define a multigraph with the
given edge multiplicities. It is equivalent to putting parallel edges on the

The "recs" attributes go beyond this, and they add to all edges (even the
multiple ones) an additional edge covariate, which can be discrete, but also

Networks with discrete edge covariates can be modeled either as a multigraph
(via eweight) or a simple graph with edge covariates. The only difference is
the functional form the model has, which is not identical.