Complex networks in the Euclidean space of communicability distances

Ernesto Estrada

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


We study the properties of complex networks embedded in a Euclidean space of communicability distances. The communicability distance between two nodes is defined as the difference between the weighted sum of walks self-returning to the nodes and the weighted sum of walks going from one node to the other. We give some indications that the communicability distance identifies the least crowded routes in networks where simultaneous submission of packages is taking place. We define an index Q based on communicability and shortest path distances, which allows reinterpreting the “small-world” phenomenon as the region of minimum Q in the Watts-Strogatz model. It also allows the classification and analysis of networks with different efficiency of spatial uses. Consequently, the communicability distance displays unique features for the analysis of complex networks in different scenarios.

Original languageEnglish
Article number066122
Number of pages11
JournalPhysical Review E
Issue number6
Publication statusPublished - 19 Jun 2012


  • complex networks
  • Euclidean space
  • communicability distances


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