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arXiv · 1412.1787

ERGMs are Hard

Michael J. Bannister·William E. Devanny·David Eppstein
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Abstract

We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a graph to be a weighted sum of feature counts. These log-likelihoods must be exponentiated and then normalized to produce probabilities, and the normalizing constant is called the \emph{partition function}. We show that the problem of computing the partition function is $\mathsf{\#P}$-hard, and inapproximable in polynomial time to within an exponential ratio, assuming $\mathsf{P} \neq \mathsf{NP}$. Furthermore, there is no randomized polynomial time algorithm for generating random graphs whose distribution is within total variation distance $1-o(1)$ of a given ERGM. Our proofs use standard feature types based on the sociological theories of assortative mixing and triadic closure.

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Michael J. Bannister, William E. Devanny, David Eppstein. 2014-12-04. ERGMs are Hard. https://arxiv.org/abs/1412.1787

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