Complex networks renormalization: flows and fixed points

Details Complex networks renormalization: flows and fixed points Complex networks renormalization: flows and fixed points

2008-03-25

arxiv.org/abs/0803.3637v2

Phys. Rev. Lett. 101, 148701 (2008)

Physics

Physics and Society

4 pages, 4 figures. Final version published on Physical Review Letters

Scientific paper

10.1103/PhysRevLett.101.148701

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.

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