How to calculate the main characteristics of random graphs - a new approach

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.