Multifractal analysis of mobile social networks

¹ School of Software, Nanchang Hangkong University - Nanchang 330063, China
² School of Mathematics And Statistics, Xi Dian University - Xian 710071, China
³ Jiang Xi Province Center for Disease Control and Prevenvion - Nanchang 330029, China

^(a) zhengwei@nchu.edu.com (corresponding author)
^(b) zzf_edu@126.com (corresponding author)
^(c) dyf_nchu@126.com (corresponding author)

Received: 15 August 2017
Accepted: 14 November 2017

Abstract

As Wireless Fidelity (Wi-Fi)-enabled handheld devices have been widely used, the mobile social networks (MSNs) has been attracting extensive attention. Fractal approaches have also been widely applied to characterierize natural networks as useful tools to depict their spatial distribution and scaling properties. Moreover, when the complexity of the spatial distribution of MSNs cannot be properly charaterized by single fractal dimension, multifractal analysis is required. For further research, we introduced a multifractal analysis method based on box-covering algorithm to describe the structure of MSNs. Using this method, we find that the networks are multifractal at different time interval. The simulation results demonstrate that the proposed method is efficient for analyzing the multifractal characteristic of MSNs, which provides a distribution of singularities adequately describing both the heterogeneity of fractal patterns and the statistics of measurements across spatial scales in MSNs.