Quantifying long-range correlations in complex networks beyond nearest neighbors

TL;DR

This paper introduces a fluctuation analysis method to measure spatial correlations in complex networks by examining degree sequences along shortest paths, revealing different correlation behaviors in models and real networks.

Contribution

It presents a novel fluctuation analysis approach to quantify long-range correlations in complex networks beyond nearest neighbors.

Findings

BA model shows exponential decay in fluctuation functions

Cayley tree and fractal networks exhibit power-law behavior

Fractal network model displays long-range anti-correlations

Abstract

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension.