Communicability in complex networks

E. Estrada, N. Hatano, Ramon y Cajal program Spain (Funder)

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Abstract

We propose a new measure of the communicability of a complex network, which is a broad generalization of the concept of the shortest path. According to the new measure, most of the real-world networks display the largest communicability between the most connected (popular) nodes of the network (assortative communicability). There are also several networks with the disassortative communicability, where the most "popular" nodes communicate very poorly to each other. Using this information we classify a diverse set of real-world complex systems into a small number of universality classes based on their structure-dynamic correlation. In addition, the new communicability measure is able to distinguish finer structures of networks, such as communities into which a network is divided. A community is unambiguously defined here as a set of nodes displaying larger communicability among them than to the rest of the nodes in the network.
Original languageEnglish
Article number036111
Number of pages12
JournalPhysical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume77
Issue number3
DOIs
Publication statusPublished - 11 Mar 2008

Keywords

  • complex networks
  • network theory (graphs)
  • set theory

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