Multifractal analysis of weighted networks by a modified sandbox algorithm

Song, Yuqin; Liu, Jinlong; Yu, Zu-Guo; Li, Bao-Gen

doi:10.1038/srep17628

Cited by 38 publications

(25 citation statements)

References 59 publications

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“…In order to determine the multifractal dimensions of our complex network, we chose this adapted sandbox algorithm because it is precise, efficient and practical. Moreover, a study by Song et al [2] has shown that this algorithm gives better results when it is used in unweighted networks, and this is our case.…”

Section: Sandbox Algorithm For Multifractal Analysis Of Complex Networksupporting

confidence: 56%

Fractal and multifractal analysis of complex networks: Estonian network of payments

et al. 2017

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Complex networks have gained much attention from different areas of knowledge in recent years. Particularly, the structures and dynamics of such systems have attracted considerable interest. Complex networks may have characteristics of multifractality. In this study, we analyze fractal and multifractal properties of a novel network: the large scale economic network of payments of Estonia, where companies are represented by nodes and the payments done between companies are represented by links. We present a fractal scaling analysis and examine the multifractal behavior of this network by using a sandbox algorithm. Our results indicate the existence of multifractality in this network and consequently, the existence of multifractality in the Estonian economy. To the best of our knowledge, this is the first study that analyzes multifractality of a complex network of payments.

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Section: Sandbox Algorithm For Multifractal Analysis Of Complex Networksupporting

confidence: 56%

Fractal and multifractal analysis of complex networks: Estonian network of payments

et al. 2017

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“…In the past few years, studies have surfaced where the concept of multifractality has been applied to complex networks [2,8,10]. In all cases, some of the networks studied required a dimension spectrum to characterise the self-similar properties.…”

Section: The Multifractal Spectrummentioning

confidence: 99%

“…We use the range of values suggested in the literature [10], starting at -10 and ending at +10, in step sizes of one.…”

Section: Algorithm 1 Sandbox Algorithm For Multifractal Analysis Of Amentioning

confidence: 99%

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Multifractality and dimensional determinism in local optima networks

Thomson

Vérel

Ochoa

et al. 2018

Proceedings of the Genetic and Evolutionary Computation Conference

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We conduct a study of local optima networks (LONs) in a search space using fractal dimensions. The fractal dimension (FD) of these networks is a complexity index which assigns a non-integer dimension to an object. We propose a fine-grained approach to obtaining the FD of LONs, using the probabilistic search transitions encoded in LON edge weights. We then apply multi-fractal calculations to LONs for the first time, comparing with mono-fractal analysis. For complex systems such as LONs, the dimensionality may be different between two sub-systems and multi-fractal analysis is needed. Here we focus on the Quadratic Assignment Problem (QAP), conducting fractal analyses on sampled LONs of reasonable size for the first time. We also include fully enumerated LONs of smaller size. Our results show that local optima spaces can be multi-fractal and that valuable information regarding probabilistic self-similarity is encoded in the edge weights of local optima networks. Links are drawn between these phenomena and the performance of two competitive metaheuristic algorithms.

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“…In [8], the box covering algorithm was designed to measure the fractal of real networks, which is named as box dimension. Box covering and box dimension of complex networks have been widely studied [9][10][11][12]. On the one hand, box dimension and box covering algorithms have been extended or modified.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Three Statistical Variables on Self-Similarity in Complex Networks

Lei

Liu

Wei

2020

Discrete Dynamics in Nature and Society

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The reason for the self-similarity property of complex network is still an open issue. In this paper, we focus on the influence of degree, betweenness, and coreness on self-similarity of complex network. Some nodes are removed from the original network based on the definitions of degree, betweenness, and coreness in the ascending and descending order. And then, some new networks are obtained after removing nodes. The self-similarities of original network and new networks are compared. Moreover, two real networks are used for numerical simulation, including a USAir network and the yeast protein interaction (YPI) network. The effects of the three statistical variables on the two real networks are considered. The results reveal that the nodes with large degree and betweenness have great effects on self-similarity, and the influence of coreness on self-similarity is small.

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Multifractal analysis of weighted networks by a modified sandbox algorithm

Cited by 38 publications

References 59 publications

Fractal and multifractal analysis of complex networks: Estonian network of payments

Fractal and multifractal analysis of complex networks: Estonian network of payments

Multifractality and dimensional determinism in local optima networks

The Influence of Three Statistical Variables on Self-Similarity in Complex Networks

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