The phases of large networks with edge and triangle constraints

  title={The phases of large networks with edge and triangle constraints},
  author={Richard W. Kenyon and Charles Radin and Kui Ren and Lorenzo A Sadun},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • R. Kenyon, C. Radin, L. Sadun
  • Published 16 January 2017
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for many of the phase transitions. All but one of the many phase transitions in this model break some form of symmetry, and we use this model to explore how changes in symmetry are related to discontinuities at these transitions. 
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