THyMe+: Temporal Hypergraph Motifs and Fast Algorithms for Exact Counting

TL;DR

This paper introduces 96 temporal hypergraph motifs and a fast exact algorithm, THyMe+, for analyzing their occurrences, enabling scalable comparison of complex, evolving group interactions across diverse real-world datasets.

Contribution

The paper defines a comprehensive set of temporal hypergraph motifs and develops THyMe+, a highly efficient algorithm for their exact counting in large hypergraphs.

Findings

THyMe+ is up to 2,163 times faster than baseline methods.

Temporal hypergraph motifs reveal domain-specific interaction patterns.

Motifs help compare structural and temporal characteristics across datasets.

Abstract

Group interactions arise in our daily lives (email communications, on-demand ride sharing, comment interactions on online communities, to name a few), and they together form hypergraphs that evolve over time. Given such temporal hypergraphs, how can we describe their underlying design principles? If their sizes and time spans are considerably different, how can we compare their structural and temporal characteristics? In this work, we define 96 temporal hypergraph motifs (TH-motifs), and propose the relative occurrences of their instances as an answer to the above questions. TH-motifs categorize the relational and temporal dynamics among three connected hyperedges that appear within a short time. For scalable analysis, we develop THyMe+, a fast and exact algorithm for counting the instances of TH-motifs in massive hypergraphs, and show that THyMe+ is at most 2,163X faster while requiring less space than baseline. Using it, we investigate 11 real-world temporal hypergraphs from various domains. We demonstrate that TH-motifs provide important information useful for downstream tasks and reveal interesting patterns, including the striking similarity between temporal hypergraphs from the same domain.