• Featured in Physics
  • Editors' Suggestion

Complex Networks Renormalization: Flows and Fixed Points

Filippo Radicchi, José J. Ramasco, Alain Barrat, and Santo Fortunato
Phys. Rev. Lett. 101, 148701 – Published 1 October 2008
Physics logo See Synopsis: Zooming out on complex networks

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 20 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.148701

©2008 American Physical Society

Synopsis

Key Image

Zooming out on complex networks

Published 6 October 2008

How the structural organization of a network evolves as it is observed on larger and larger scales remains an open question. Now, a general and systematic approach to answer this question may be in sight.

See more in Physics

Authors & Affiliations

Filippo Radicchi1, José J. Ramasco1, Alain Barrat1,2,3, and Santo Fortunato1

  • 1Complex Systems Lagrange Laboratory (CNLL), ISI Foundation, Torino, Italy
  • 2Laboratoire de Physique Théorique (CNRS UMR 8627), Université de Paris-Sud, France
  • 3CPT (CNRS UMR 6207), Luminy Case 907, F-13288 Marseille Cedex 9, France

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 101, Iss. 14 — 3 October 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×