How would one best interpret the min_dl value returned by

minimize_nested_blockmodel_dl and minimize_blockmodel_dl when a multigraph

(weighted) graph is processed? The min_dl for a multigraph can be much lower

for the same graph without multiplicities. What is a reasonable way to

explain, using the min_dl values, that a multigraph version of graph

produces a "better" (or not) description of the same graph without

multiplicities?

Crudely, you should think of the edges as the "data points" which are

being used to fit a model. If you add more of them, especially if you

keep the number of nodes fixed, you should get a better fit. Now, if the

additional edges do not follow exactly the same distribution as the

previous ones, they can either reduce or increase the description length

per edge. If the new edges are more randomly distributed, the DL/E will

increase, and if they are more ordered it will decrease.

Note that this only applies to the DL per edge. The total non-normalized

DL will always increase if more edges are added.

Best,

Tiago