Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
Determination of multifractal dimensions of complex networks by means of the sandbox algorithm
复制标题
利用沙箱算法确定复杂网络的多重分形维数
作者：
Liu, Jin-Long;Yu, Zu-Guo;Vo Anh
复杂网络在科学技术的各个领域引起了人们的极大关注。多重分形分析(MFA)是系统描述理论和实验分形图空间异质性的一种有效方法。在本文中，我们使用了由tel等人提出的沙盒算法。(Physica A 159,155-166(1989))，用于复杂网络的MFA。首先，将SB算法与现有的两种用于复杂网络的MFA算法进行了比较：Furuya和Yakubo(Phys.E.84,036118(2011年))，以及Li等人提出的改进的计盒算法。(J.Stat.机甲：理论。实验2014，P02020(2014))通过计算一些确定性模型网络的质量指数tau(Q)。我们对这些模型网络的数值结果和理论结果进行了详细的比较。比较结果表明，SB算法是计算质量指数tau(Q)和探索复杂网络多重分形行为最有效、最可行的算法。然后，我们应用SB算法研究了一些经典模型网络的多重分形性质，如无标度网络、小世界网络和随机网络。结果表明，无标度网络存在多重分形性，小世界网络的多重分形性不明显，随机网络几乎不存在多重分形性。(C)2015 AIP出版有限责任公司。
Complex networks have attracted much attention in diverse areas of science and technology. Multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we employ the sandbox (SB) algorithm proposed by Tel et al. (Physica A 159, 155-166 (1989)), for MFA of complex networks. First, we compare the SB algorithm with two existing algorithms of MFA for complex networks: the compact-box-burning algorithm proposed by Furuya and Yakubo (Phys. Rev. E 84, 036118 (2011)), and the improved box-counting algorithm proposed by Li et al. (J. Stat. Mech.: Theor. Exp. 2014, P02020 (2014)) by calculating the mass exponents tau(q) of some deterministic model networks. We make a detailed comparison between the numerical and theoretical results of these model networks. The comparison results show that the SB algorithm is the most effective and feasible algorithm to calculate the mass exponents tau(q) and to explore the multifractal behavior of complex networks. Then, we apply the SB algorithm to study the multifractal property of some classic model networks, such as scale-free networks, small-world networks, and random networks. Our results show that multifractality exists in scale-free networks, that of small-world networks is not obvious, and it almost does not exist in random networks. (C) 2015 AIP Publishing LLC.