基于网络拓扑结构的重要节点发现算法

复杂网络中的重要节点发现在现实生活中有着广泛的应用价值。传统重要节点发现方法可分为局部发现和全局发现两类算法,全局发现算法中最具代表性的是特征向量中心性算法(Eigenvector Centrality, EC),EC算法将所有节点归为一个社区并利用邻居节点重要性反馈计算节点的影响力大小,具有较高的计算效率和识别精度。但是,EC算法忽略了网络的拓扑结构,未考虑到真实网络中节点所在社区的结构特征。为此,本文提出一种基于网络拓扑结构的可达中心性算法(Accessibility Centrality, AC),首先利用邻接矩阵作为反馈路径,在反馈过程中计算不同路径下的节点整体影响力。同时,利用影响力传递过程中的噪音干扰特性,修正每一路径长度下节点整体影响力大小,最后利用修正结果得到AC值。为评估AC算法,本文利用两种传染病模型模拟节点影响力在四组真实网络中的传播过程,并引入其他四种算法进行对比验证。实验结果表明,与其他算法相比,AC算法可以更准确、有效地识别出有具有影响力的重要节点。     

复杂网络在双曲空间的节点动态择优路径研究

本文研究复杂网络双曲嵌套模型.利用改进克林伯格和克莱尔科夫网络拓扑模型的方法,得到了复杂网络在双曲空间的动态择优路径,推广和发展了复杂网络节点间最优路径的算法.     

用牵制控制方法进行含随机噪声的复杂网络的拓扑结构识别

本文研究了含噪声的复杂动态网络的拓扑结构识别的问题.利用牵制控制(Pinning控制)方法,基于随机微分方程的理论基础,来进行网络的拓扑结构识别,设计自适应反馈控制器和识别率,来反演网络结构,通过数值仿真,获得了pinning控制方法主要是通过一部分未知节点来识别整个网络的拓扑结构的结果,噪声强度的范围将影响网络结构正确识别时的耦合强度范围,噪声强度越大,可识别的耦合强度也越大.     

基于加权局域世界的金融网络演化模型研究

在加权局域世界网络模型的基础上,文章将复杂网络与金融系统相结合,提出一种新局域世界的加权金融网络模型.其主要思想是在加权局域世界网络中引入了服从指数分布的增长方式和双向择优选择的连边方式.利用平均场理论和仿真模拟得到网络节点度、强度和权值都服从幂律分布,其分布指数与所取参数有关.通过网络拓扑性质的研究和沪市A股股票数据的实证研究,发现该金融网络模型具有层次结构和异配特性,与实际网络具有相似的拓扑结构.     

蛋白质相互作用网络的多参数模糊关系分析

分析蛋白质相互作用网络的拓扑结构特征与生物进化之间的关系,并用于预测蛋白质的功能是后基因时代重要的研究课题.本文提出了基于模糊数学理论的蛋白质网络多种拓扑属性模糊关系数学模型,并应用频数分析算法将无序的模糊关系数据进行序列化.通过分析蛋白质网络拓扑属性模糊关系参数可以为研究生物进化与蛋白质网络结构之间的关系提供数据基础,同时也为预测未知蛋白质的功能奠定了基础.该方法为研究蛋白质网络进化和标记蛋白质的功能开拓了一个新的方向.     

尾部风险网络视角下的金融机构系统性风险贡献研究

金融机构的尾部风险关联模式及结构在金融系统性风险的形成演化中发挥重要作用。利用CoVaR指标及分位数回归方法,衡量金融机构之间的尾部风险传染强度,进而建立金融机构尾部风险动态网络。分析全连接网络及阈值法下过滤网络的全局和局部拓扑结构特征及其动态演化规律。建立面板数据回归模型,研究网络拓扑结构特征对金融机构系统性风险贡献的影响。实证研究发现,全连接网络的节点强度,能有效地衡量金融机构尾部风险传染强度及承受强度,并揭示其动态变化规律;各机构的尾部风险传染强度及承受强度排序匹配性存在差异;随着时间推进,各金融机构间的平均尾部风险传染路径缩短、系统性风险更易迅速累积和爆发;滞后一期的节点出度、节点入度及聚集系数越大,相应金融机构的系统性风险贡献越小;滞后一期的节点介数和节点接近中心度越大,相应金融机构的系统性风险贡献越大。研究结果对于金融机构的宏观审慎监管及系统性风险管理,提供了一个全新的基于金融机构尾部风险网络的视角。     

基于冰情检测环境的无线传感器网络路由协议研究

结合冰凌测报无线传感器网络中传感器节点能量受限、节点随着冰凌的产生与流动会出现在河道断面局部观测区域的冰凌测报无线传感器网络拓扑结构不断变化这一特性,提出了对贪婪周边无状态路由协议GPSR的改进策略GFSRI(GPSR-Improved),改进算法中采用图论模型,借助网络模拟器NS2(Network Simulator 2),对GPSR算法以及改进的路由策略GPSRI进行了模拟仿真实验,对路由算法中涉及到的关键参数的相关实验数据进行了处理分析.模拟仿真实验及评估结果表明,GPSRI在数据包转发的路由跳数、源和目的节点间端到端的传输时延方面与GPSR相比有较大的性能改进.     

多社团加权复杂网络建模及其级联抗毁性研究

为了研究社团结构和权重因素对网络级联抗毁性的影响,引入节点和边的消亡机制,建立了一类具有社团结构的加权网络模型.采用本方法生成网络的度、强度和边权分布都呈现无标度特性,比现有BBV (Barrat-Barthelemy-Vespignani)模型具有更好的社团结构特性,且幂律指数、模块度参数可调.在此基础上研究了网络的级联抗毁性,采用节点及其邻居节点强度的函数定义网络负荷,故障节点负荷采用"局部定义,局部分配"的策略.仿真分析了边权演化参数、模块度函数、攻击策略和演化时间对网络级联抗毁性的影响.结论表明,网络的抗毁性与边权演化参数、网络演化时间成反比,与模块度的关系不是单调的而是存在一个阈值.优先攻击度最大节点的策略对网络抗毁性破坏最大,且在多节点遭受攻击时,网络的故障规模会发生突变.文章的研究结论对故障的预防与控制以及网络的建设具有一定的参考价值.     

基于TOPSIS模型的机场网络节点重要度评估

在机场网络中单个机场节点的失效往往会对其他的节点产生影响,特别是关键节点的失效会波及整个网络.准确客观的识别重要节点机场关乎整个机场网络的安全运营.本文分析了机场网络拓扑特性中的度、集聚系数和接近度指标,考虑了机场旅客吞吐量和所在城市人口等交通经济特性指标,使用熵权法确定权重的基础上,应用TOPSIS法构建综合评价体系模型,最后以华东地区机场网络为例进行节点重要度排序.结果表明与单一指标的评估结果相比,该方法更加全面客观的确定不同属性指标的权重,避免了不同指标取值的差异性,使评价更加全面,更符合机场网络实际运营情况.     

基于改进节点重要度引力模型的航路网拥堵节点识别

航路网络存在一些关键航路点对系统整体具有重要控制作用,而有效辨识这些重要节点对缓解空中交通拥堵,提高航路运行效率具有极大意义.以复杂网络理论为基础,从网络视角结合中心度及节点服务能力通过改进传统引力模型进行节点重要度评估;然后基于改进节点重要度引力模型进行航路网络拥堵节点识别仿真,并将结果与传统介数法进行对比验证.研究表明:改进的引力模型识别的重要节点,不仅具有较大的中心度,且较多位于航路网络流量较大位置;基于引力模型识别航路网络节点重要度的准确率更高,在提高网络通行率基础上更及时地识别航路网络易拥堵节点,对预防节点失效、减少航路网络拥堵具有积极作用.     

Lag projective synchronization of a class of complex network constituted nodes with chaotic behavior

In this paper, a method of the lag projective synchronization of a class of complex network constituted nodes with chaotic behavior is proposed. Discrete chaotic systems are taken as nodes to constitute a complex network and the topological structure of the network can be arbitrary. Considering that the lag effect between network node and chaos signal of target system, the control input of the network and the identification law of adjustment parameters are designed based on Lyapunov theorem. The synchronization criteria are easily verified.     

Generalized Topological Essentiality and Coincidence Points of Multivalued Maps

A concept of generalized topological essentiality for a large class of multivalued maps in topological vector Klee admissible spaces is presented. Some direct applications to differential equations are discussed. Using the inverse systems approach the coincidence point sets of limit maps are examined. The main motivation as well as main aim of this note is a study of fixed points of multivalued maps in Fréchet spaces. The approach presented in the paper allows to check not only the nonemptiness of the fixed point set but also its topological structure.      

Functional centrality in graphs

In this article, we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure.     

Nodal degenerations of plane curves and galois covers

Globally irreducible nodes (i.e. nodes whose branches belong to the same irreducible component) have mild effects on the most common topological invariants of an algebraic curve. In other words, adding a globally irreducible node (simple nodal degeneration) to a curve should not change them a lot. In this paper we study the effect of nodal degeneration of curves on fundamental groups and show examples where simple nodal degenerations produce non-isomorphic fundamental groups and this can be detected in an algebraic way by means of Galois covers.      

Linear-time compression of 2-manifold polygon meshes into information-theoretically optimal number of bits

The polygon mesh is an important primitive used in representing 3D models. Its specification consists of topological and geometrical quantities; where the former describes the connection nodes, edges and faces, and the latter describes attributes such as node positions, face colors, etc. Our interest here lies with the encoding of the topology. Specifically, this paper presents a linear-time information-theoretically optimal compression algorithm for encoding a planar 2-manifold polygon mesh to a bit string X.     

Systematic Measures of Biological Networks II: Degeneracy,Complexity, and Robustness

This paper is part II of a two‐part series devoted to the study of systematic measures in a complex bionetwork modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological network including degeneracy, complexity, and robustness. We will apply the theory of stochastic differential equations to define degeneracy and complexity for a bionetwork. Robustness of the network will be defined according to the strength of attractions to the global attractor. Based on the study of stationary probability measures and entropy made in part I of this series, we will investigate some fundamental properties of these systematic measures, in particular the connections between degeneracy, complexity, and robustness.© 2016 Wiley Periodicals, Inc.     

Graph Collapsing in Shortest Path Auction Algorithms

In this paper we consider the problem of finding a shortest path from a source node to a fixed target node (SSP) or to all the nodes (SPT) on a directed graph. A family of algorithms which derives from the known auction algorithm is introduced. The key feature of these algorithms is based on topological transformations operated on the graphs that replace an optimal sub-path with a single arc of the same length (graph collapsing concept). The same idea is applied both to the standard auction algorithm and to a modified version of the algorithm. In the last mentioned case a good saving in computation cost is obtained as shown by the reported numerical examples.     

Natural synchronization in power-grids with anti-correlated units

Synchronization between spatially distributed nodes of a power-grid is a crucial requirement for its proper operation. Using a Kuramoto-like network as a realistic physical model for the distribution of electrical power in a power-grid, we obtain coupling strengths and topological characteristics that favor the synchronous state of those technological networks. Power-grids are highly heterogeneous. They are composed of different classes of nodes and each node behaves differently. We show in this work that if a power-grid is extensive and nodes are highly connected, the coupling strength that leads to synchronization depends mainly on the eigenvalues of the Laplacian matrix, as it happens in homogeneous networks composed of equal nodes. On the other hand, if a power-grid is sparsely connected, the coupling strength that leads to synchronization is also strongly related to the correlation coefficient of the network, which means that a high number of connections between similar nodes (two power plants or two consumer centers) disfavor the synchronizability of the power-grid. We apply our results to the Brazilian power-grid system.