Modeling non-Poissonian temporal hypergraphs by Markovian node dynamics

TL;DR

This paper introduces Markovian node-based models for temporal hypergraphs, explaining bursty event sequences and correlations in group interactions through stochastic node activity states.

Contribution

It provides analytical derivations of interevent time distributions and autocorrelations, linking individual node dynamics to observed temporal patterns in hypergraphs.

Findings

Event processes are mixtures of Poissonian and short-tailed components.

Interevent time distributions become longer-tailed despite Markovian dynamics.

Model predictions align with empirical data on group interactions.

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.