Nonparametric Modeling of Higher-Order Interactions via Hypergraphons

Let V {1,..., n} be a set of n items that could represent for example, people in a social network, genes in a biological network or researchers in academic networks. Models of interaction among the n items could be conveniently represented in the form of a graph or a hypergraph, G(V, E), where the items form the nodes of the graph and the hyperedge set E represents the interactions among the items. Network datasets that capture such complex interactions between a set of objects are becoming increasingly prevalent in several scientific fields. Developing realistic generative models for such networks is a challenging problem that has been an active subject of research across diverse fields spanning from statistics, physics, computer science; see Kolaczyk (2009); Goldenberg et al. (2010); Battiston et al. (2020) for comprehensive overview. A majority of the existing work has focussed on the case of modeling pairwise interactions.