Principles of statistical mechanics of random networks

Abstract We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges.

• Publication year

  2002

• Venue

  arXiv.org

• Publication date

  2002-04-04

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1016/S0550-3213(03)00504-2arXiv cond-mat/0204111
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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