Scale Free Networks from Self-Organisation

Details Scale Free Networks from Self-Organisation Scale Free Networks from Self-Organisation

2004-11-15

arxiv.org/abs/cond-mat/0411390v2

Phys.Rev.E 72 (2005) 26138

Physics

Condensed Matter

Statistical Mechanics

33 Pages. Revised discussion of finite size effects

Scientific paper

10.1103/PhysRevE.72.026138

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of parameters. The growth mechanism is based on using local graph information only, so this is a process of self-organisation. The standard mean-field equations are an excellent approximation for network growth using these rules. We discuss the effects of finite size on the degree distribution, and compare analytical results to simulated networks. Finally, we generalise the random walk algorithm to produce weighted networks with power-law distributions of both weight and degree.

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