Structural properties of random networks with hidden variables

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.