Small-world to fractal transition in complex networks: A renormalization group approach

Hernán D. Rozenfeld, Chaoming Song, Hernán A. Makse

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


We show that renormalization group (RG) theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world-fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a nontrivial point of a pure fractal topology that is stable or unstable according to the amount of long-range links in the network, and (iii) another stable point of a fractal with shortcuts that exist exactly at the small-world-fractal transition. As a collateral, the RG technique explains the coexistence of the seemingly contradicting fractal and small-world phases and allows us to extract information on the distribution of shortcuts in real-world networks, a problem of importance for information flow in the system.

Original languageEnglish (US)
Article number025701
JournalPhysical Review Letters
Issue number2
StatePublished - Jan 11 2010
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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