Emergence of Global Preferential Attachment From Local Interaction

TL;DR

This paper demonstrates that global preferential attachment in networks can emerge from local interaction rules, challenging the assumption that individuals need global information to shape network growth.

Contribution

It shows that local interaction models like DDPA, acquaintance, and CNN can produce global preferential attachment, revealing local contact as a fundamental mechanism.

Findings

Global attachment emerges from local models.

Attachment rate depends linearly or sublinearly on degree.

Empirical email networks support local contact influence.

Abstract

Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this paper, it is found that the global preferential attachment emerges from the local interaction models, including distance-dependent preferential attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys. Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A. Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the attachment rate depends linearly on the degree or strength, while for acquaintance network model, the dependence follows a sublinear power law. It implies that for the evolution of social networks, local contact could be more fundamental than the presumed global preferential attachment. This is onsistent with the result observed in the evolution of empirical email networks.