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2014

$\beta$ models for random hypergraphs with a given degree sequence

Stasi, Despina, Sadeghi, Kayvan, Rinaldo, Alessandro et al.

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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.

$\beta$ models for random hypergraphs with a given degree sequence · Around

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On random graphs
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Discrete Multivariate Analysis: Theory and Practice
Y. M. M. Bishop, S. E. Fienberg, and P. W. Holland · 1975
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Paul Holland, Samuel Leinhardt. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association , 76:33–50, 1981
1981
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Michal Karonski and Tomasz Luczak. The phase transition in a random hypergraph. Journal of Computational and Applied Mathematics , 142:125—135, 2002
2002
Earlier work this paper cites.

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