Complex networks renormalisation: flows and fixed points
Résumé
Complex networks in nature, society and technology share a set of topological features, reflecting some common organisational principles. Recently, it has been claimed that some complex networks are self-similar under a convenient renormalisation procedure. Here we present a general method to systematically study renormalisation flows in graphs. We find that the behaviour of some variables under renormalisation, such as the maximum and the average number of connections of a node, is described by simple scaling laws, characterised by critical exponents. This result holds for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalisation flows for graphs display features similar to those found in the well-known renormalisation of spin systems. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graph topologies that are inaccessible to a standard analysis.
Domaines
Physique et Société [physics.soc-ph]
Origine : Fichiers produits par l'(les) auteur(s)