Modeling temporal hypergraphs

2025-06-02

AI Summary

Analyzing the statistical significance of higher-order interactions in temporal hypergraphs remains challenging due to the lack of principled null models that accurately preserve higher-order structural features over time. Method: We propose the Relational Hyper-Event Model (RHEM), the first framework to construct a null distribution with precise control over temporal hyperedge structural properties. RHEM defines a vector of temporal hyperedge statistics—including subset repetition, higher-order triangle closure, homophily, and higher-order degree assortativity—and employs moment-matching constrained optimization to enable controllable generation of complex patterns and deviation detection. Contribution/Results: Unlike conventional null models relying solely on node-degree distributions, RHEM supports expectation constraints and significance testing for arbitrary-order substructures, ensuring reproducibility and interpretability. It provides a unified, flexible, and scalable statistical framework for structural attribution and anomaly detection in temporal higher-order networks.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Computational social science

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. 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.

Problem

• Modeling temporal hypergraphs with higher-order interactions
• Defining null distributions using relational hyperevent models
• Analyzing overrepresentation of hyperedge configurations statistically

Innovation

• Modeling temporal hypergraphs with RHEM
• Tailored null distributions for hypergraphs
• Analyzing hyperedge configurations statistically