The origin of preferential attachment and the generalized preferential attachment for weighted networks
arXiv:physics/0608063 · doi:10.1016/j.physa.2006.11.082
Abstract
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.
17 pages, 4 figures, final version, Physica A, 377, 709, 2007
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