Interpreting min_dl (min value of nats per edge) for blockmodel on multigraphs

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

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.