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Mean-field solution of equilibrium ensembles of undirected networks with 3-edge interactions

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Peter Fleck, Center for Complex Systems Research, Department of Physics, University of Illinois at Urbana-Champaign
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We study the equilibrium statistical mechanics of ensembles of undirected networks with triangle- and 3-star-type interaction among bi-valued edges.
We present analytical expressions for the statistics' averages in mean-field approximation.
We find this model's phase diagram to be identical after parameter substitution to that of a model with triangle interactions only.
Both interactions affect the network's topology very similarly.
We find the mean-field solution to agree excellently with Markov Chain Monte Carlo simulations in an important part of parameter space.
Implications for the analysis of network topologies are being discussed.