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Center for Nonlinear Studies |
A family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble, will be presented. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network properties subject to the constraints imposed by a given set of observations. Exact solutions of models within this class that incorporate arbitrary degree distributions and arbitrary but independent edge probabilities will be given. Also discussed are some more complex examples with correlated edges that can be solved approximately or exactly by adopting various familiar methods, including mean-field theory, perturbation theory, and saddle-point expansions.