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

TL;DR

This paper demonstrates that local growth rules in networks naturally lead to linear preferential attachment and explain properties like clustering hierarchy and degree correlations, supported by analytical and numerical evidence.

Contribution

It shows that local rules in network growth models can produce global properties like preferential attachment, clustering, and degree correlations, unifying local mechanisms with observed network features.

Findings

Local rules lead to effective linear preferential attachment.

Local models explain clustering hierarchy in networks.

Numerical and analytical results support local rules' role in network properties.

Abstract

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.