Gabel, A.,Krapivsky, P. L.,Redner, S.
We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node at to a randomly chosen 'target,' node with probability 1 - r. or to the parent of the target, node With probability r. When the redirection probability r is an increasing function of the degree of the parent node, with r -> 1 as the parent degree diverges, net Works grown via this enhanced redirection mechanism exhibit unusual properties, including (1) multiple macrohubs. i.e.. nodes with degrees proportional to the number of network nodes N; non-extensivity of the degree distribution in which the number of nodes of degree k, N-k, scales a Nv-1/k(v), with 1 < v < 2; (iii) lack of self-averaging, with large fluctuations between individual network realizations. These features are robust and continue to hold when the incoming node has out-degree greater than 1 so that networks contain closed loops. The latter networks are strongly clustered; for the specific case of double attachment, the average local clustering coefficient is < C-i > = 4ln2 - 2 = 0.77258….