Statistics of weighted treelike networks
- 21 March 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 71 (3) , 036124
- https://doi.org/10.1103/physreve.71.036124
Abstract
We study the statistics of growing networks with a tree topology in which each link carries a weight , where and are the node degrees at the end points of link . Network growth is governed by preferential attachment in which a newly added node attaches to a node of degree with rate . For general values of and , we compute the total weight of a network as a function of the number of nodes and the distribution of link weights. Generically, the total weight grows as for and superlinearly otherwise. The link weight distribution is predicted to have a power-law form that is modified by a logarithmic correction for the case . We also determine the node strength, defined as the sum of the weights of the links that attach to the node, as function of . Using known results for degree correlations, we deduce the scaling of the node strength on and .
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