Physics Colloquium
Monday, March 11th, 2005, 4:00 P.M.

Hernan Makse

Levich Institute and Physics Department, City College of New York

Complex Networks are Self-Similar

Complex networks have been studied extensively due to their relevance to many real world systems as diverse as the World Wide Web (WWW), the Internet, social networks and biological networks in which molecules interact to keep a cell alive. A large number of real complex networks are given the name "scale-free" because they show a power-law degree distribution. However, it is widely believed that complex networks are not length-scale invariant or self-similar, a conclusion that originates from the "small world" property of these networks. Nevertheless, here we present a novel approach to the analysis of such networks, revealing that their structure is indeed self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a finite fractal dimension. These fundamental properties suggest a common self-organization dynamics of diverse networks at different scales into a critical state and in turn bring together previously unrelated fields: the statistical physics of complex networks with renormalization, fractals and critical phenomena.

Reference: C. Song, S. Havlin and H. A. Makse, Nature 433, 392 (2005).

http://lisgi1.engr.ccny.cuny.edu/~makse/