Configuration models of random hypergraphs

Abstract

AbstractMany empirical networks are intrinsically polyadic, with interactions occurring within groups of agents of arbitrary size. There are, however, few flexible null models that can support statistical inference in polyadic networks. We define a class of null random hypergraphs that hold constant both the node degree and edge dimension sequences, thereby generalizing the classical dyadic configuration model. We provide a Markov Chain Monte Carlo scheme for sampling from these models and discuss connections and distinctions between our proposed models and previous approaches. We then illustrate the application of these models through a triplet of data-analytic vignettes. We start with two classical topics in network science—triadic clustering and degree-assortativity. In each, we emphasize the importance of randomizing over hypergraph space rather than projected graph space, showing that this choice can dramatically alter both the quantitative and qualitative outcomes of statistical inference. We then define and study the edge intersection profile of a hypergraph as a measure of higher-order correlation between edges, and derive asymptotic approximations for this profile under the stub-labeled null. We close with suggestions for multiple avenues of future work. Taken as a whole, our experiments emphasize the ability of explicit, statistically grounded polyadic modelling to significantly enhance the toolbox of network data science.