Renormalization flows in complex networks
Radicchi, F, Barrat, A, Fortunato, S, Ramasco, JJPhys. Rev. E 79, 026104 (2009)
Times cited: 9
Abstract
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.