Let a clique be a subset of the vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. Let a maximal clique be a set of vertices that is a clique and also a maximal set.

I'm open to answers that defer to the research study's operational definition of "relationship" in such networks. For example, either in-person or virtual relationships are fine. Social media networks are fine.

I am not asking about the mathematics of the model itself, nor about its computation. Tools like NetworkX provide options for computation. Rather, I am asking if there are any instances of it in Sociology research, especially in an international context.

We might analogize to factor analysis, which is a commonly-used model in Psychometrics. Factor analysis can be described quite precisely in terms of Linear Algebra and mathematical statistics.

Questions about estimator bias or matrix multiplication in factor analysis would be off-topic here. But, factor analysis is not off-topic when it intersects with its use in understanding IQ or the g-factor.

Have any international estimates been made for the frequency distribution over the size (cardinalities) of the maximal cliques that humans participate in?



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