Correlation dimension of complex 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