Solution of the 2-star model of a network

Abstract

The p-star model or exponential random graph is among the oldest and best-known of network models. Here we give an analytic solution for the particular case of the 2-star model, which is one of the most fundamental of exponential random graphs. We derive expressions for a number of quantities of interest in the model and show that the degenerate region of the parameter space observed in computer simulations is a spontaneously symmetry broken phase separated from the normal phase of the model by a conventional continuous phase transition.

5 pages, 3 figures

References in corpus (8)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Random graphs with arbitrary degree distributions and their applications
• The origin of degree correlations in the Internet and other networks
• Correlated random networks
• Network Transitivity and Matrix Models
• Statistical mechanics of topological phase transitions in networks

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