Multipodal Phases in Dense Networks
Radin, C. UT Austin, USA
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We consider asymptotically large, dense, simple graphs constrained in both their edge and triangle densities, and study the associated entropy, the goal being to determine the structure of `exponentially most' graphs with given variable constraints. We have proven there is a sharp phase transition between graphs of large versus low edge density E, at any fixed triangle density T, when T=E^3. Simulations show that the high edge density regime is further broken up into well-defined regions which are overwhelmingly dominated by graphs of very simple `multipodal' structure, simple modifications of balanced multipartite graphs. This is joint work with Kui Ren and Lorenzo Sadun.