Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

TL;DR

This paper explores the multifractal cross-correlation properties of vertex observables in complex networks, revealing distinctive patterns that differentiate network models and relate to real-world protein contact networks.

Contribution

It introduces a multifractal cross-correlation analysis method to characterize nonlinear coupling effects in network vertex time series.

Findings

Distinct multifractal properties identify different network models.

Protein contact networks share features with scale-free and small-world models.

Unique cross-correlation signatures distinguish Erdős-Rényi, Barabási-Albert, and Watts-Strogatz networks.

Abstract

We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased random walks. We consider three vertex properties that provide, respectively, short, medium, and long-range information regarding the topological role of vertices in a given network. In order to reveal the relation between these quantities, we applied the multifractal cross-correlation analysis technique, which provides information about the nonlinear effects in coupling of time series. We show that the considered network models are characterized by unique multifractal properties of the cross-correlation. In particular, it is possible to distinguish between Erd\"{o}s-R\'{e}nyi, Barab\'{a}si-Albert, and Watts-Strogatz networks on the basis of fractal cross-correlation. Moreover, the analysis of protein contact networks reveals characteristics shared with both scale-free and small-world models.