ArticleScientific reports2015
Multifractal analysis of weighted networks by a modified sandbox algorithm.
Article in Scientific reports, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- A bivariate multifractal analysis approach to understanding socio-spatial segregation dynamics.Scientific reports · 2025Article
- Multifractality of Complex Networks Is Also Due to Geometry: A Geometric Sandbox Algorithm.Entropy (Basel, Switzerland) · 2023Article
- An Extended Correlation Dimension of Complex Networks.Entropy (Basel, Switzerland) · 2021Article
- A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems.Biomaterials · 2019Review
- Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications.Scientific reports · 2017Article
- Fractal and multifractal analyses of bipartite networks.Scientific reports · 2017Article
- Dynamic-Sensitive centrality of nodes in temporal networks.Scientific reports · 2017Article
- The fractal heart - embracing mathematics in the cardiology clinic.Nature reviews. Cardiology · 2017Review
Corrections and comments
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Authors and funding
4 authors.
Funding
No grant is acknowledged in the PubMed record.
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.
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Registered trials
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