Correlation dimension of complex networks

TL;DR

This paper introduces a novel method to measure the dimension of complex networks using a dynamical systems approach based on random walks, extending the Grassberger-Procaccia algorithm for network analysis.

Contribution

It presents a new correlation dimension measure for complex networks derived from ergodic theory, applicable to both synthetic and real-world networks, and computationally efficient.

Findings

Effective for synthetic and real-world networks

Provides reliable dimension estimates

Fast computation relying on local walker information

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.