Small world-Fractal Transition in Complex Networks: Renormalization Group Approach

Details Small world-Fractal Transition in Complex Networks: Renormalization Group Approach Small world-Fractal Transition in Complex Networks: Renormalization Group Approach

2009-09-26

arxiv.org/abs/0909.4832v2

Phys. Rev. Lett. 104, 025701 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevLett.104.025701

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.

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