Abstract
Phys. Rev. Lett. 104, 025701 (2010) We show that renormalization group (RG) theory applied to complex networks
are 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 non-trivial 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 short-cuts that exists 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 to extract information on the distribution of short-cuts in real-world
networks, a problem of importance for information flow in the system.
