Solution of the 2-star model of a network

Details Solution of the 2-star model of a network Solution of the 2-star model of a network

2004-05-19

arxiv.org/abs/cond-mat/0405457v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevE.70.066146

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.

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