  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.
