Characteristic exponents of complex networks

TL;DR

This paper introduces a new method to analyze complex networks by examining the statistical properties of random walk trajectories, enabling classification and property identification of networks.

Contribution

It proposes a novel approach using characteristic exponents derived from random walk time series to characterize network structure and dynamics.

Findings

Characteristic exponents effectively distinguish different network types

Method captures both local and global network organization

Framework aids in classifying networks and understanding growth properties

Abstract

We present a novel way to characterize the structure of complex networks by studying the statistical properties of the trajectories of random walks over them. We consider time series corresponding to different properties of the nodes visited by the walkers. We show that the analysis of the fluctuations of these time series allows to define a set of characteristic exponents which capture the local and global organization of a network. This approach provides a way of solving two classical problems in network science, namely the systematic classification of networks, and the identification of the salient properties of growing networks. The results contribute to the construction of a unifying framework for the investigation of the structure and dynamics of complex systems.