Entangled networks, super-homogeneity and optimal network topology
Abstract
A new family of graphs, Entangled Networks, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for generic dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. They are characterized as well by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure (poor modularity). More importantly, we show that this family of nets exhibits an excellent performance with respect to other connectivity or flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, good searchability, efficient communication, etc. These remarkable features convert entangled networks in a powerful and useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications in network design, computer science, or neuroscience.Keywords
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