2002/04/30 by S. N. Dorogovtsev, S.N. Dorogovtsev, J. F. F. Mendes +3 · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Construct (python library) #Degree (music) #Opinion Dynamics and Social Influence #Partition (number theory) #Partition function (quantum field theory) #Simple (philosophy) #Statistical mechanics #Theoretical and Computational Physics #Uncorrelated #cond-mat.stat-mech #cs.NI #hep-lat #hep-th #math-ph #math.MP #nlin.AO
paper · pdf · doi:10.1016/s0550-3213(03)00504-2
published as Nucl.Phys. B666 (2003) 396-416 · 14 pages, an extended version
arxiv created 2002/12/29 · openalex publication_date 2003/07/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.