复杂网络的重分形分析算法研究及其应用

发布时间：2018-04-12 19:28

本文选题：复杂网络 + 二分网络　；参考：《湘潭大学》2017年博士论文

【摘要】：复杂网络已经吸引了来自科学技术不同领域研究者的大量关注。继复杂网络中的小世界特性与无标度性质之后,自相似性已经成为复杂网络的第三大基本特征并且在近年来得到了广泛的研究。分形分析可以有效地揭示一些分形对象的自相似性。然而,重分形分析是一个用来系统性地刻画理论和实验复杂分形对象空间异质性的更加强大而有效的工具。尽管已有一些研究复杂网络自相似性的分形和重分形分析算法,但是这些算法的效率并不高而且已有的算法并不是对所有类型的复杂网络总是有效的。因此,研发高效、可行、精确的分形和重分形分析算法以及针对特殊类型的网络提出特殊的算法显得尤为重要。在本文中,我们改进分形几何中已有的沙箱算法(sandbox algorithm)去研究复杂网络的重分形性质。首先我们通过计算一些确定性模型网络的质量指数τ(q)去将改进的沙箱算法与已有的两个重分形分析算法进行了比较,这两个算法分别是改进的紧盒子燃烧算法(compact-box-burning algorithm)和改进的计盒算法(box-counting algorithm)。我们对这些确定性模型网络的质量指数τ(q)的理论解和由这三个算法计算得到的数值结果做了详细的比较。比较结果显示改进的沙箱算法对于计算网络的质量指数τ(q)并进一步研究复杂网络的重分形性质是最有效、最可行的。然后,我们使用改进的沙箱算法去研究了其他一些经典模型网络的重分形性质,包括无标度网络、小世界网络与随机网络。数值结果表明在无标度网络中存在重分形性质,重分形性质在小世界网络中并不明显,而随机网络则几乎不具有重分形性质。最近,二分网络(bipartite network)也已经引起了不同领域研究者的大量兴趣。单分网络(unipartite network)或者经典网络(classical network)的分形和重分形性质在近年来已经得到了研究,但是目前还没有工作去研究二分网络的这些性质。在本文中,我们通过对大量真实二分网络数据集和由一些二分网络模型生成的二分网络进行分形和重分形分析试图去揭示二分网络的自相似结构。首先,我们发现在一些二分网络中存在分形性质,包括CiteULike、Netflix、MoieLens(ml-20m)、Delicious真实二分网络数据集和由(u,v)-flower模型所生成的第7代(2, 2)-flower二分网络。同时,我们也发现并不是所有二分网络都具有明显的自相似性,即在其他几个二分网络中观察到了偏移幂律和指数行为。我们接下来研究了二分网络的重分形性质。结果表明上面具有分形性质的二分网络还具有重分形性质。为了捕捉二分网络包含两类不同节点的本质特征,我们受到推荐系统中基于网络资源配置动力学的启发给二分网络中不同类的节点赋予了不同的权重。重分形分析的结果显示这些节点加权二分网络存在重分形性质。另外,对于带评分的二分网络数据集,我们构建了对应的边加权二分网络。相应地,已有的两个用来研究边加权单分网络分形和重分形性质的算法被修改以使得它们能够用于去研究这些边加权二分网络的自相似性。研究结果表明这些修改的算法是可行的,能够有效地揭示这些边加权二分网络和相应的节点加权二分网络的自相似结构。最后,我们把修改的算法用于去研究几个已经常被其他研究人员所研究的无权单分网络的分形和重分形性质。我们的分形结果和之前的研究结果是一致的。因此,这些修改的算法也能有效地用来研究无权单分网络的自相似性。
[Abstract]:Complex networks have attracted a lot of attention from various fields of science and technology. The following small world properties in complex networks and scale-free properties, self similarity has become the third basic characteristics of complex networks and has been widely studied in recent years. The fractal analysis can effectively reveal the self similarity of fractal object. However, multifractal analysis is used to systematically describe the theory and experiment of complex fractal object spatial heterogeneity is more powerful and effective tool. Although there have been some research on Fractal and multifractal analysis algorithm of self similar complex networks, but the efficiency of these algorithms is not high and the existing algorithm is not all types of complex networks is effective. Therefore, developing an efficient, feasible, and put forward the algorithm for a special type of network analysis accurate fractal and multifractal A special algorithm is particularly important. In this paper, we improved the existing algorithm of fractal geometry in the sandbox (sandbox algorithm) to study the multifractal properties of complex networks. We calculate the quality index of some deterministic model of network tau (q) to two multifractal algorithm with the existing sand box improved analysis algorithm comparing the two algorithms are tight box improved burning algorithm (compact-box-burning algorithm) and the improved box counting algorithm (box-counting algorithm). Our quality index of these networks is a deterministic model (q) theory solution and the numerical calculated by the three algorithm results made a detailed comparison. Comparison results show that the improved algorithm for computing network sandbox quality index (q) the multifractal properties and further the study of complex networks is the most effective, the most feasible. Then, we use the The improved algorithm to study the sandbox multifractal properties of some other classical models including network, scale-free network, small world network and the random network. The numerical results show that the existence of multifractal properties in scale-free networks, multifractal properties in the small world network and the random network is not obvious, little has multifractal nature. Recently, two network (bipartite network) has attracted a lot of interest of researchers in different fields. A single network (unipartite network) or classical network (classical network) the fractal and multifractal properties have been studied in recent years, but there is no work to study these properties of two networks. In this paper, we based on a large number of real data sets and two network generated by some two network models of two sub networks of fractal and multifractal analysis to reveal the two network Self similar network structure. Firstly, we found that there are some two points in the fractal property of the network including CiteULike, Netflix, MoieLens, Delicious (ml-20m) two real network data set and by (U, V) -flower model generated by the seventh generation (2, 2) -flower two network. At the same time, we also found that not all two networks have obvious self similarity, i.e. the observed power-law index and migration behavior in several other two points in the network. Then we study the multifractal properties of two sub networks. The results show that the two points above the network with fractal properties has multifractal properties in order to capture. Two different types of nodes of the network includes two essential features, we are inspired by the cyber source to different types of dynamic configuration of two nodes in the network gives different weights based on recommendation system. The results of multifractal analysis show that these day Two point weighted network has multifractal properties. In addition, the two network data with the score set, we constructed two points corresponding to the edge weighted network. Accordingly, the two has been used to study the single edge weighted network fractal and multifractal properties of the algorithm are modified to make them can be used for self similar to study these two edge weighted network. The results show that the modified algorithm is feasible and can effectively reveal the self similar structure of these two edge weighted network and the corresponding node weighted two points of the network. Finally, we have modified the fractal method is applied to study several other researchers have often been the right to a single network and multifractal properties. The results of our research on Fractal and previous results are consistent. Therefore, the modified algorithm can be effectively used to study a single network from unauthorized Similarity.

【学位授予单位】：湘潭大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O157.5

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