Entangled networks, synchronization, and optimal network topology

Details Entangled networks, synchronization, and optimal network topology Entangled networks, synchronization, and optimal network topology

2005-02-09

arxiv.org/abs/cond-mat/0502230v3

Phys. Rev. Lett. 95, 188701 (2005)

Physics

Condensed Matter

Statistical Mechanics

Slightly modified version, as accepted in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.95.188701

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications computer science or neuroscience.

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