Multifractal analysis and topological properties of a new family of weighted Koch networks
Multifractal analysis and topological properties of a new family of weighted Koch networks
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DOI：
10.1016/j.physa.2016.11.032
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发表时间：
2017-03
影响因子：
3.3
通讯作者：
Da-Wen Huang;Zuguo Yu;V. Anh
中科院分区：
文献类型：
--
作者：
Da-Wen Huang;Zuguo Yu;V. Anh
加权复杂网络，特别是无标度网络，比非加权网络更能表征现实系统，近年来引起了相当大的兴趣。对加权复杂网络的多重分形问题的研究仍有待开展。本文受Koch网络和Koch岛概念的启发，提出了一种新的加权Koch网络族，并研究了它们的多重分形行为和拓扑性质。我们发现了新网络的一些关键拓扑性质：它们的顶点累积强度具有幂律分布；它们的拓扑度与权重强度呈幂律关系；在大代t的极限下，网络具有0.41004的高加权聚类系数（与比例因子c无关）；对于一般拉普拉斯算子，第二小特征值μ 2和最大特征值μ n近似为尺度因子c的四次多项式，而对于归一化拉普拉斯算子，μ 2近似为尺度因子c和μ n= 1.5的四次多项式。然后，我们发现加权koch网络既是分形的又是多重分形的，其分形维数受尺度因子c的影响。我们还将这些分析应用于六个现实网络，发现其中三个网络的多重分形很强。
Weighted complex networks, especially scale-free networks, which characterize real-life systems better than non-weighted networks, have attracted considerable interest in recent years. Studies on the multifractality of weighted complex networks are still to be undertaken. In this paper, inspired by the concepts of Koch networks and Koch island, we propose a new family of weighted Koch networks, and investigate their multifractal behavior and topological properties. We find some key topological properties of the new networks: their vertex cumulative strength has a power-law distribution; there is a power-law relationship between their topological degree and weight strength; the networks have a high weighted clustering coefficient of 0.41004 (which is independent of the scaling factor c) in the limit of large generation t; the second smallest eigenvalue μ 2 and the maximum eigenvalue μ n are approximated by quartic polynomials of the scaling factor c for the general Laplacian operator, while μ 2 is approximately a quartic polynomial of c and μ n= 1.5 for the normalized Laplacian operator. Then, we find that weighted koch networks are both fractal and multifractal, their fractal dimension is influenced by the scaling factor c. We also apply these analyses to six real-world networks, and find that the multifractality in three of them are strong.