Conjecture on the facets of the network model cone
Let denote the model matrix for the directed random graph network model with reciprocation, and let be its cone. For a network on nodes, the facets conjecture. has facets: correspond to patterns of zeros leading to a zero row or column margin, and the remaining correspond to patterns of zeros that cause the maximum-likelihood estimate not to exist without inducing zero margins. This conjecture is based on computations in \texttt{polymake} for networks of size up to ; a general proof is not provided in the source.
References
Primary source
A. Rinaldo, S. Petrović and S. E. Fienberg, “On the Existence of the MLE for a Directed Random Graph Network Model with Reciprocation”, arXiv:1010.0745 (2010).
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