Quantifying long-range correlations in complex networks beyond nearest neighbors

¹  Potsdam Institute for Climate Impact Research - 14412 Potsdam, Germany, EU
²  Levich Institute, City College of New York - New York, NY 10031, USA
³  Division of Natural Sciences, College of Mount Saint Vincent - Riverdale, NY 10471, USA

Corresponding author: ca-dr@rybski.de

Received: 20 November 2009
Accepted: 9 April 2010

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 anticorrelations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension.