Temporal hypergraph motifs

Abstract

Group interactions arise in our daily lives (email communications, on-demand ride sharing, and 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 THmotifs in massive hypergraphs, and we show that THYME+ is up to 2,163x faster while requiring less space than baseline approaches. In addition to exact counting algorithms, we design three versions of sampling algorithms for approximate counting. We theoretically analyze the accuracy of the proposed methods, and we empirically show that the most advanced algorithm, THYME-A*, is up to 11.1x more accurate than baseline approaches. Using the algorithms, 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.