Complex networks renormalization: Flows and fixed points
Radicchi, F, Ramasco, JJ, Barrat, A, Fortunato, SPhys. Rev. Lett. 101, 148701 (2008)
Times cited: 30
Abstract
Recently, it has been claimed that some complex networks are
self-similar under a convenient renormalization procedure. We present a
general method to study renormalization flows in graphs. We find that
the behavior of some variables under renormalization, such as the
maximum number of connections of a node, obeys simple scaling laws,
characterized by critical exponents. This is true for any class of
graphs, from random to scale-free networks, from lattices to
hierarchical graphs. Therefore, renormalization flows for graphs are
similar as in the renormalization of spin systems. An analysis of
classic renormalization for percolation and the Ising model on the
lattice confirms this analogy. Critical exponents and scaling functions
can be used to classify graphs in universality classes, and to uncover
similarities between graphs that are inaccessible to a standard
analysis.