Modeling non-Poissonian temporal hypergraphs by Markovian node dynamics
Abstract
Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce node-driven temporal hypergraph models in which each node stochastically alternates between low- and high-activity states, and a hyperedge produces time-stamped events with a probability that depends on the number of high-state nodes in the hyperedge. For two event-generation rules, we analytically derive interevent time distributions and autocorrelation functions of event sequences, both for hyperedges and nodes. Despite Markovian node-state dynamics, the induced event processes become mixtures of Poissonian, short-tailed components, resulting in longer-tailed interevent time distributions and slowly decaying autocorrelation. The theory further shows the dependence of these features on the size of hyperedge, which largely agrees with various empirical data. We expect our models to provide a simple, interpretable framework for connecting individual-level activity fluctuations to the timing patterns observed in real group interactions.
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BibTeX
@article{jo2026modeling,
title = {{Modeling non-Poissonian temporal hypergraphs by Markovian node dynamics}},
author = {Hang-Hyun Jo and Naoki Masuda},
journal = {Communications Physics},
year = {2026},
month = oct,
doi = {10.1038/s42005-026-02885-0},
url = {https://www.nature.com/articles/s42005-026-02885-0},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Modeling non-Poissonian temporal hypergraphs by Markovian node dynamics
AU - Hang-Hyun Jo
AU - Naoki Masuda
PY - 2026
DA - 2026/10/21
JO - Communications Physics
DO - 10.1038/s42005-026-02885-0
UR - https://www.nature.com/articles/s42005-026-02885-0
AB - Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce node-driven temporal hypergraph models in which each node stochastically alternates between low- and high-activity states, and a hyperedge produces time-stamped events with a probability that depends on the number of high-state nodes in the hyperedge. For two event-generation rules, we analytically derive interevent time distributions and autocorrelation functions of event sequences, both for hyperedges and nodes. Despite Markovian node-state dynamics, the induced event processes become mixtures of Poissonian, short-tailed components, resulting in longer-tailed interevent time distributions and slowly decaying autocorrelation. The theory further shows the dependence of these features on the size of hyperedge, which largely agrees with various empirical data. We expect our models to provide a simple, interpretable framework for connecting individual-level activity fluctuations to the timing patterns observed in real group interactions.
SN - 2399-3650
ER -