The origin of preferential attachment and the generalized preferential attachment for weighted networks

Details The origin of preferential attachment and the generalized preferential attachment for weighted networks The origin of preferential attachment and the generalized preferential attachment for weighted networks

2006-08-06

arxiv.org/abs/physics/0608063v3

Physica A, 377, 709-716, 2007

Physics

Physics and Society

17 pages, 4 figures, final version, Physica A, 377, 709, 2007

Scientific paper

10.1016/j.physa.2006.11.082

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network, which makes it is neither entirely degree preferential nor entirely weight preferential. Second, it can tell us not only the chance that each already-existing vertex being connected but also how much weight each new edge has. The generalized preferential attachment can generate four power-law distributions, besides the three for vertex degrees, vertex strengths, and edge weights, it yield a new power-law distribution for the subgraph degrees.

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