• Corpus ID: 239998123

Typical large graphs with given edge and triangle densities

  title={Typical large graphs with given edge and triangle densities},
  author={Joe Neeman and Charles Radin and Lorenzo A Sadun},
. The analysis of large simple graphs with extreme values of the densities of edges and triangles has been extended to the statistical structure of typical graphs of fixed inter-mediate densities, by the use of large deviations of Erd˝os-R´enyi graphs. We prove that the typical graph exhibits sharp singularities as the constraining densities vary between different curves of extreme values, and we determine the precise nature of the singularities. The ex-tension to graphs with fixed densities of… 

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