Phase transitions in a complex network

@article{Radin2013PhaseTI,
  title={Phase transitions in a complex network},
  author={Charles Radin and Lorenzo A Sadun},
  journal={Journal of Physics A},
  year={2013},
  volume={46},
  pages={305002}
}
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then determine the optimizing graphs for small triangle density and a range of edge density, though we can only prove they are local, not global, maxima of the entropy density. With this assumption we then prove that the resulting entropy density must lose its… 
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