title: Small-world to fractal transition in complex networks: a renormalization group approach.
abstract: 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.
authors.affiliation: Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
authors.forename: Hernán D
authors.initials: HD
authors.lastname: Rozenfeld
authors.forename: Chaoming
authors.initials: C
authors.lastname: Song
authors.forename: Hernán A
authors.initials: HA
authors.lastname: Makse