Renormalization flows in complex networks

Details Renormalization flows in complex networks Renormalization flows in complex networks

2008-11-17

arxiv.org/abs/0811.2761v2

Phys. Rev. E 79, 026104 (2009)

Physics

Physics and Society

12 pages, 11 figures

Scientific paper

10.1103/PhysRevE.79.026104

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

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