Modeling temporal hypergraphs

TL;DR

This paper introduces a flexible modeling framework for temporal hypergraphs using relational hyperevent models (RHEM), enabling analysis of complex dependencies and configurations in dynamic higher-order networks.

Contribution

It presents how RHEM can be used to define null models for temporal hypergraphs, allowing for testing complex structural dependencies beyond traditional metrics.

Findings

RHEM can specify expected hyperedge statistics matching observed data.

The framework allows testing for over- or underrepresentation of hypergraph configurations.

Applications include analyzing preferential attachment, triadic closure, and homophily.

Abstract

Networks representing social, biological, technological or other systems are often characterized by higher-order interaction involving any number of nodes. Temporal hypergraphs are given by ordered sequences of hyperedges representing sets of nodes interacting at given points in time. In this paper we discuss how a recently proposed model family for time-stamped hyperedges - relational hyperevent models (RHEM) - can be employed to define tailored null distributions for temporal hypergraphs and to test and control for complex dependencies in hypergraph dynamics. RHEM can be specified with a given vector of temporal hyperedge statistics - functions that quantify the structural position of hyperedges in the history of previous hyperedges - and equate expected values of these statistics with their empirically observed values. This allows, for instance, to analyze the overrepresentation or underrepresentation of temporal hyperedge configurations in a model that reproduces the observed distributions of possibly complex sub-configurations, including but going beyond node degrees. Concrete examples include, but are not limited to, preferential attachment, repetition of subsets of any given size, triadic closure, homophily, and degree assortativity for subsets of any order.