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Multifractal analysis of weighted networks by a modified sandbox algorithm

机译:改进的沙箱算法对加权网络进行多重分形分析

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摘要

Complex networks have attracted growing attention in many fields. As a generalization of fractal 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): “” WFNs and “” 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.
机译:复杂的网络已在许多领域吸引了越来越多的关注。作为分形分析的概括,(MFA)是一种有用的方法,可以系统地描述理论和实验分形图案的空间异质性。过去几年中已经提出了一些针对非加权复杂网络的MFA的算法,包括我们小组最近采用的沙盒(SB)算法。本文针对加权网络的MFA提出了一种改进的SB算法(称为SBw算法)。首先,我们使用SBw算法研究两个加权分形网络(WFN)系列的多重分形特性:“” WFN和“” WFN。我们还将讨论分形维数和广义分形维数如何随WFN的边缘权重而变化。通过对这些网络的理论分形维数和数值分形维数进行比较,我们发现所提出的SBw算法对于加权网络的MFA是有效且可行的。然后,我们将SBw算法应用于研究某些实际加权网络(协作网络)的多重分形特性。发现多重分形存在于这些加权网络中,并且受其边缘权重的影响。

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