title: Multifractal analysis of weighted networks by a modified sandbox algorithm.
abstract: Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks. First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks - collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.
authors.affiliation: Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China.|College of Science, Hunan University of technology, Zhuzhou, Hunan 412007, China.
authors.forename: Yu-Qin
authors.initials: YQ
authors.lastname: Song
authors.affiliation: Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China.
authors.forename: Jin-Long
authors.initials: JL
authors.lastname: Liu
authors.affiliation: Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China.|School of Mathematical Sciences, Queensland University of Technology, Brisbane, Q4001, Australia.
authors.forename: Zu-Guo
authors.initials: ZG
authors.lastname: Yu
authors.affiliation: Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China.
authors.forename: Bao-Gen
authors.initials: BG
authors.lastname: Li