Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations

Details Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations

2002-11-24

arxiv.org/abs/cond-mat/0211528v2

Phys. Rev. E 67, 056104 (2003)

Physics

Condensed Matter

Statistical Mechanics

17 pages, 14 figures (to appear in Phys. Rev E)

Scientific paper

10.1103/PhysRevE.67.056104

The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a general principle based on local rules. In this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules. It is also shown that the local models offer an explanation to other properties like the clustering hierarchy and degree correlations recently observed in complex networks. These conclusions are based on both analytical and numerical results of different local rules, including some models already proposed in the literature.

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