Article abstract

Nature Physics 2, 275 - 281 (2006)

Subject Category: Statistical physics, thermodynamics and nonlinear dynamics

Origins of fractality in the growth of complex networks

Chaoming Song1, Shlomo Havlin2 and Hernán A. Makse1

Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.

  1. Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA
  2. Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel

Correspondence to: Hernán A. Makse1 e-mail:


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