Multifractal Measures on Small-World Networks

TL;DR

This paper explores the multifractal properties of first passage times in small-world networks, revealing how rewiring fraction influences the presence of multifractality and identifying a critical threshold.

Contribution

It introduces a method to estimate multifractal measures of first passage times on small-world networks with varying rewiring fractions.

Findings

Fractal dimension D_0 estimated around 0.92 for specific network parameters.

Multifractal properties vanish beyond a critical rewiring fraction p_c.

Rewiring fraction significantly affects the multifractal nature of the network.

Abstract

We investigate the multifractals of the normalized first passage time on one-dimensional small-world network with both reflecting and absorbing barriers. The multifractals is estimated from the distribution of the normalized first passage time charactrized by the random walk on the small-world network with three fractions of edges rewired randomly. Particularly, our estimate is the fractal dimension D_0 = 0.917, 0.926, 0.930 for lattice points L = 80 and a randomly rewired fraction p = 0.2. The numerical result is found to disappear multifractal properties in the regime p> p_c, where p_c is the critical rewired fraction.