Motifs in temporal hypergraphs
Abstract
Network motifs, recurrent local patterns of interactions in graphs, provide fundamental insights on the interplay between structure and functionality in complex systems. Many real-world systems are not well represented by traditional static pairwise networks, as interactions may involve groups of nodes, occur over time, or encode directionality. In this paper, we introduce temporal motifs for hypergraphs and directed hypergraphs, extending motif analysis to timestamped many-body interactions. We formalize the corresponding mining problem, study the combinatorial structure of these motifs, and develop exact algorithms for their enumeration. In particular, we propose a dynamic programming algorithm that substantially reduces the computational cost of motif mining, achieving orders of magnitude speedups on empirical datasets. We also introduce a null model for temporal hypergraphs to assess the statistical over- and under-expression of motifs. Applying the proposed framework to real-world datasets from different domains, including face-to-face contacts, scientific collaborations, e-mail exchanges, and Bitcoin transactions, we show that temporal hypergraph motifs reveal distinct forms of local organization across systems. Finally, we demonstrate their use as an exploratory tool through focused case studies on persistent patterns in scientific collaborations and e-mail communications.
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BibTeX
@misc{lotito2026motifs,
title = {{Motifs in temporal hypergraphs}},
author = {Quintino Francesco Lotito and Lorenzo Betti and Federico Battiston and Giuseppe Francesco Italiano},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12175},
eprint = {2609.12175},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12175},
}
RIS
TY - UNPB
TI - Motifs in temporal hypergraphs
AU - Quintino Francesco Lotito
AU - Lorenzo Betti
AU - Federico Battiston
AU - Giuseppe Francesco Italiano
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12175
UR - https://arxiv.org/abs/2609.12175
AB - Network motifs, recurrent local patterns of interactions in graphs, provide fundamental insights on the interplay between structure and functionality in complex systems. Many real-world systems are not well represented by traditional static pairwise networks, as interactions may involve groups of nodes, occur over time, or encode directionality. In this paper, we introduce temporal motifs for hypergraphs and directed hypergraphs, extending motif analysis to timestamped many-body interactions. We formalize the corresponding mining problem, study the combinatorial structure of these motifs, and develop exact algorithms for their enumeration. In particular, we propose a dynamic programming algorithm that substantially reduces the computational cost of motif mining, achieving orders of magnitude speedups on empirical datasets. We also introduce a null model for temporal hypergraphs to assess the statistical over- and under-expression of motifs. Applying the proposed framework to real-world datasets from different domains, including face-to-face contacts, scientific collaborations, e-mail exchanges, and Bitcoin transactions, we show that temporal hypergraph motifs reveal distinct forms of local organization across systems. Finally, we demonstrate their use as an exploratory tool through focused case studies on persistent patterns in scientific collaborations and e-mail communications.
ER -