Random networks created by biological evolution.

We investigate a model of an evolving random network, introduced by us previously [Phys. Rev. Lett. 83, 5587 (1999)]. The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that the underlying network can evolve by adding and removing sites. The behavior and the averaged properties of the network depend on the parameter p, the probability to establish a link to the newly introduced site. For p=1 the system is self-organized critical, with two distinct power-law regimes with forward-avalanche exponents tau=1.98+/-0.04 and tau(')=1.65+/-0.05. The average size of the network diverges as a powerlaw when p-->1. We study various geometrical properties of the network: the probability distribution of sizes and connectivities, size and number of disconnected clusters, and the dependence of the mean distance between two sites on the cluster size. The connection with models of growing networks with a preferential attachment is discussed.