Analysis of Complex Networks

2.4 Ensembles of Random Networks – Superstatistics

The simplest example for a (re-)wiring rule is the class of random networks introduced by Erdös and Rényi [1, 2], where N nodes are fully randomly connected by a set of L links. This corresponds to attaching a unique linking probability to each node, i.e., is the probability that any possible given pair of nodes is linked. The corresponding degree distribution is the binomial distribution

which in the large N limit reduces to the Poissonian distribution, , where again λ = = (N–1) ~ L/N. At this step one could introduce additional limitations on states, such as forbidding, e.g., self-linking, c_ii = 0. In the large N limit such limitations are of marginal importance.

In the Erdös–Rényi case each node has the same probability of being linked to any other node. In many realistic situations this is not the case and the linking probability of ...