Statistics of Weighted Networks

Details Statistics of Weighted Networks Statistics of Weighted Networks

2004-08-12

arxiv.org/abs/cond-mat/0408295v2

Phys. Rev. E 71, 036124 (2005)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures, 2-column revtex4 format. Version 2 has an additional figure and minor changes in response to referee comme

Scientific paper

10.1103/PhysRevE.71.036124

We study the statistics of growing networks in which each link carries a weight (k_i k_j)^theta, where k_i and k_j are the node degrees at the endpoints of link ij. Network growth is governed by preferential attachment in which a newly-added node attaches to a node of degree k with rate A_k=k+lambda. For general values of theta and lambda, we compute the total weight of a network as a function of the number of nodes N and the distribution of link weights. Generically, the total weight grows as N for lambda>theta-1, and super-linearly otherwise. The link weight distribution is predicted to have a power law form that is modified by a logarithmic correction for the case lambda=0. We also determine the node strength, defined as the sum of the weights of the links that attach to the node, as function of k. Using known results for degree correlations, we deduce the scaling of the node strength on k and N.

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