Configuration Models of Random Hypergraphs

Abstract

Many 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 for such polyadic networks. We define a class of null random hypergraphs that hold constant both the node degree and edge dimension sequences, 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 these models through a triplet of applications. We start with two classical network topics -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 statistical inference and study findings. 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 under the stub-labeled null. Our experiments emphasize the ability of explicit, statistically-grounded polyadic modeling to significantly enhance the toolbox of network data science. We close with suggestions for multiple avenues of future work.

Nonlinearity + Networks: A 2020 Vision

“…For example, a scientist can be adjacent to a paper that they have written [119], and a legislator can be adjacent to a committee on which they sit [144]. It is important to generalize ideas from graph theory to hypergraphs, such as by developing models of random hypergraphs [25,26,52].…”

Hypernetwork Science via High-Order Hypergraph Walks

“…In comparison to their graph counterparts, generative hypergraph models are relatively few. Nonetheless, researchers have recently begun developing a wider variety of hypergraph models, both for the case of uniform hypergraphs [15,16,17,55] and non-uniform hypergraphs [11,19,20,26,35]. In the present work, we consider three generative hypergraph models from [2], which can be thought of as hypergraph interpretations of the graph models Erdős-Rényi (ER) [22], Chung-Lu (CL) [13], and Block Two-Level Erdős-Rényi (BTER) [41,63].…”

Micro-level network dynamics of scientific collaboration and impact: relational hyperevent models for the analysis of coauthor networks

“…The time ordering is meaningful when analyzing coauthor networks since collaboration probabilities, or the expected impact of collaboration, might depend, among others, on previous publication activity, shared activity, or prior success. A second characteristic is that interaction events in coauthor networks are intrinsically polyadic (Chodrow 2019;Chodrow & Mellor 2020), that is, they involve sets of actors of any size, rather than relating exactly two actors at a time. Ignoring the multi-actor aspect of coauthoring assumes potentially invalid independence of dyads and can lead to information loss.…”