English

Correlation dimension of complex networks

Physics and Society 2015-06-12 v2 Statistical Mechanics Social and Information Networks

Abstract

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

Keywords

Cite

@article{arxiv.1211.2651,
  title  = {Correlation dimension of complex networks},
  author = {Lucas Lacasa and Jesus Gomez-Gardeñes},
  journal= {arXiv preprint arXiv:1211.2651},
  year   = {2015}
}

Comments

New version with a supplementary material attached, accepted for publication in Physical Review Letters

R2 v1 2026-06-21T22:36:51.656Z