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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!

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What you're looking for is the subject of this gem by Peel, Larremore and Clauset: The ground truth about metadata and community detection. See the section where they introduce the blockmodel entropy significance test. I dont know of an implementation in R, but Leto's original implementation is in matlab on his Github.

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  • $\begingroup$ It seems that the significance test BESTest takes an "NxN undirected network adjacency matrix. Code will check to ensure that the matrix is either symmetric or triangular." This is still better than any other leads I have, but it looks like I'd have to lose the directed aspect of my networks. $\endgroup$ – Andrew Feb 19 at 0:07
  • $\begingroup$ Ok, sorry I missed that. Its probably possible to generalize their method to directed stochastic block models. I'll mess around with it over the next few days to see. $\endgroup$ – ComplexGates Feb 19 at 15:52

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