Highly Dispersed Networks by Enhanced Redirection

We introduce a class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the parent of the target with probability r, where r is an increasing function of the degree of the parent. This mechanism leads to highly dispersed networks with unusual properties: (i) existence of multiple macrohubs-nodes whose degree is a finite fraction of the total number of network nodes N, (ii) lack of self-averaging, and (iii) anomalous scaling, in which N(k), the number of nodes of degree k scales as N(k)~N(ν-1)/k(ν), with 1<ν<2.