A mean-field approach to some Internet-like random networks

A conditionally Poissonian power-law random graph with infinite degree variance is considered as a random network model. A method for elegant analytical computation of accurate approximations for various network characteristics is introduced, based on slight redefinition of the model in terms of non-homogeneous Poisson point processes and on the replacement of certain random variables by their expectations. The applications include characterization of the `top clique' around the node of highest capacity, density of nodes falling outside of the giant component of the random graph, availability of disjoint paths and the distribution of traffic in the network, assuming a traffic matrix following a gravity rule.