So, I have several directed (multi-edged) networks, and within them each node has been assigned to one of seven categories (based on some a priori circumstances). Each category should have a higher within-category interaction rate, but I want to test the statistical significance of this.
Since "a set of nodes, densely connected internally" is pretty much the definition of a community, I want to manually impose my community assignments on the nodes in the network and then test whether this assignment is statistically more "community-like" than a random assignment. In essence, my question is: "Is this given community structure statistically significant?"
I found this paper which seems to have a way of measuring the statistical significance of a single community group in the network, but it doesn't seem to apply to a given, entire community structure. I also found this baby, but it seems to only be focused on much smaller, local structures.
There's gotta be a way to do this for directed, multi-edged networks, I just can't seem to find any! (Additionally, I'll have to do this analysis in R, so mega-triple-extra bonus points if you know of an R package that already does this.)
Thanks in advance!