A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.
$\beta$ models for random hypergraphs with a given degree sequence
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abstract
We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and fixed point algorithm, prove that both algorithms converge if maximum likelihood estimator (MLE) exists, and provide algorithmic and geometric ways of dealing the issue of MLE existence.
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nlin.AO 1years
2026 1verdicts
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Self-consistent analysis of the Kuramoto model with higher-order interactions
A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.