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Phys Rev Lett. 2005 Oct 28;95(18):188701. Epub 2005 Oct 24.

Entangled networks, synchronization, and optimal network topology.

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Departamento de Electromagnetismo y Física de la Materia, Instituto Carlos I de Física Teórica y Computacional, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain.


A new family of graphs, entangled networks, with optimal properties in many respects, is introduced. By definition, their topology is such that it 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 in computer science or neuroscience.

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