Origins of fractality in the growth of complex networks

Details Origins of fractality in the growth of complex networks Origins of fractality in the growth of complex networks

2005-07-08

arxiv.org/abs/cond-mat/0507216v2

Nature Physics 2, pp275 - 281 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1038/nphys266

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.

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