2003/08/29 by Agata Fronczak, Fronczak, Agata, Piotr Fronczak +3
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0308629
A poster presented at Midterm Conference COSIN - Conference on Growing Networks and Graphs in Statistical Physics, Finance, Biology and Social Systems, Roma 1-5 September 2003
arxiv created 2003/08/29 · arxiv updated 2009/12/01
The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the main network characteristics like: the position of the phase transition at which a giant component first forms, the mean component size below the phase transition, the size of the giant component and the average path length above the phase transition. Although most of the enumerated properties were previously calculated by means of generating functions, we think that our derivations are conceptually much simpler.