My talk will be devoted to a general class of random networks in which vertices are characterized by hidden variables that control establishment of edges between pairs of nodes. The above mentioned networks have been recently introduced by M. Baguna and R. Pastor-Satorras (Phys. Rev. E vol. 68 p. 036112 (2003)). The authors showed that such diverse networks like classical random graphs proposed by Erdos and Renyi (1959) and scale-free evolving networks introduced by Barabasi and Albert (1999) may be described by a common formalism.
During my talk I will present an analytic formalism describing metric properties of random uncorrelated networks with hidden variables. I will show that 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.