Renormalization flows in complex networks

Filippo Radicchi1, Alain Barrat1,2, Santo Fortunato1 and José J. Ramasco1
1Complex Systems Lagrange Laboratory, Complex Networks (CNLL), ISI Foundation, Turin I-10133, Italy.
2CPT (CNRS UMR 6207), Luminy Case 907, F-13288 Marseille Cedex 9, France

(Nov. 2008)

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.