Scale-free networks emerging from multifractal time series

TL;DR

This paper explores how multifractal properties of time series influence the topology of networks derived from them, revealing conditions under which scale-free networks emerge, supported by analytical and numerical evidence.

Contribution

It introduces a method linking multifractal time series to network topology, providing analytic conditions for the emergence of scale-free networks.

Findings

Scale-free networks can emerge from multifractal time series.

Analytic expressions relate multifractal measures to network degree.

Numerical simulations validate the theoretical predictions.

Abstract

Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic or strange attractors, on the topology of a suitably projected network. Relying on the box counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology, and validate our findings with extensive numerical simulations.