一种基于效率矩阵的网络节点重要度评价算法

为了实现对网络节点重要性的有效评价,提出一种基于网络效率矩阵的节点重要度评价算法.该方法综合考虑节点的度值(局部重要度)和网络节点之间的重要性贡献(全局重要度),利用节点的度和效率矩阵表征网络节点的重要度贡献,克服重要性贡献矩阵法中节点只依赖于邻接节点的不足.考虑实际网络的稀疏性,该算法的时间复杂度为O(n²).通过算例分析验证了该算法的可行性和有效性,结果表明:该算法能够更加直观、简单有效地区分节点的重要度差异,并且对于大型复杂网络具有较理想的计算能力.     

手机短信网络的生长过程研究

模拟了短信网络的生长过程并研究其拓扑结构.发现短信网络在生长过程中，度分布、节点的度与其加入网络时间的关系、平均度随时间的变化等方面与先前的模型有所不符.根据短信网络的数据分析，提出了短信网络的生长机制——局部优先连接机制.结果表明，模拟以短信网络为代表的实际网络时，局部优先连接模型优于其他网络模型. 关键词： 复杂网络 短信网络 局部优先连接     

利用重要度评价矩阵确定复杂网络关键节点

为了对复杂网络节点重要度进行评估,针对节点删除法、节点收缩法和介数法的不足,通过定义节点效率和节点重要度评价矩阵, 提出了一种利用重要度评价矩阵来确定复杂网络关键节点的方法.该方法综合考虑了节点效率、节点度值和相邻节点的重要度贡献,用节点度值和效率值来表征其对相邻节点的重要度贡献,其优化算法的时间复杂度为O(Rn²). 实验分析表明该方法可行有效,对于大型复杂网络可以获得理想的计算能力.     

利用节点效率评估复杂网络功能鲁棒性

为了克服现有复杂网络鲁棒性研究模型只考虑节点失效的局部影响性和网络拓扑鲁棒性的缺陷, 提出了一种利用节点效率来评估复杂网络功能鲁棒性的方法. 该方法综合考虑节点失效的全局影响性, 利用网络中节点的效率来定义各节点的负载、极限负载和失效模型, 通过打击后网络中最终失效节点的比例来衡量网络的功能鲁棒性, 并给出了其评估优化算法. 实验分析表明该方法对考虑节点负载的复杂网络功能鲁棒性的评定可行有效, 对于大型复杂网络可以获得理想的计算能力.     

基于领域相似度的复杂网络节点重要度评估算法

节点重要性度量对于研究复杂网络鲁棒性与脆弱性具有重要意义.大规模实际复杂网络的结构往往随着时间不断变化,在获取网络全局信息用于评估节点重要性方面具有局限性.通过量化节点局部网络拓扑的重合程度来定义节点间的相似性,提出了一种考虑节点度以及邻居节点拓扑重合度的节点重要性评估算法,算法只需要获取节点两跳内的邻居节点信息,通过计算邻居节点对之间的相似度,便可表征其在复杂网络中的结构重要性.基于六个经典的实际网络和一个人工的小世界网络,分别以静态与动态的方式对网络进行攻击,通过对极大连通系数与网络效率两种评估指标的实验结果对比,证明了所提算法优于基于局域信息的度指标、半局部度指标、基于节点度及其邻居度的WL指标以及基于节点位置的K-shell指标.     

全光网络的路由扩展方法

本文主要讨论了通信网络的路由创建方法,提出了一种使用节点的相邻关系来创建新路由的原理和操作步骤.在网络连接度满足一定要求后,可以重复用该方法来获得网络节点之间的所有可能路由.文章最后讨论了路由扩展方法在通信网络创建路由时的使用方法.     

基于模体的复杂网络测度量研究

针对复杂网络拓扑结构中模体的存在性, 在传统的顶点度和边聚类系数定义的基础上, 提出了基于模体的顶点度和边度来衡量网络中顶点和边的重要性. 用Rand-ESU算法对不同规模的8个网络进行模体检测, 验证了网络中模体的存在性, 重点分析了Karate网络和Dolphin网络中模体的结构和特征. 用Pearson相关系数衡量基于模体的顶点度与传统顶点度、基于模体的边度与边聚类系数的相关性, 仿真分析结果表明相关性大小与模体种类有关, 基于模体的顶点度和边度是对原定义的一种改进和拓展, 更全面地刻画了顶点和边在网络中的重要性. 关键词： 模体 顶点度 边度 Pearson相关系数     

基于有限资源提升网络可生存性的拓扑重构方法

给定网络拓扑结构和有限添加边资源,如何优化配置添加边使重构后的网络拓扑结构具有最优可生存性是非常有价值的研究问题.本文首先明确网络可生存性的量化评估指标,以移除节点后网络结构的鲁棒性和有效性为优化目标,提出网络拓扑重构优化问题的建模与分析方法.同时在给定资源代价的约束下,为实现添加边资源配置效率的最大化,提出优先配置节点加强保护圈的启发式算法.仿真实验表明,该算法在有限资源约束的随机局部故障和选择性攻击环境中,能兼顾改善网络鲁棒性和传输效率,有效提升网络结构的可生存性.     

虚拟社区网络的演化过程研究

模拟了虚拟社区网络的演化过程并研究其拓扑结构.发现虚拟社区网络在演化过程中,节点的加入、边的加入、网络中度分布、节点的度与其加入网络时间的关系、平均度随时间的变化等方面与传统的无标度网络有所不符.根据国内某论坛的实际网络数据统计与分析,提出了虚拟社区网络的演化机理——虚拟社区网络构造算法.仿真结果表明,模拟以互联网论坛为代表的虚拟社区网络时,该模型能够得到与真实网络相符的特性. 关键词： 复杂网络 虚拟社区 无标度网络     

无标度复杂网络负载传输优化策略

提出了一种能够显著提高无标度复杂网络负载传输性能的优化路由策略.实现了负载在核心节点与边缘节点间的合理分配.分析表明该策略使得网络的负载处理能力正比于网络规模的平方,而与单个节点的度值无关.实验结果显示优化路由策略在保持了最短路由策略小世界效应的同时,成倍地提升了网络的负载传输能力,且随着网络平均节点度的增加其优势越趋显著.此外,与有效路由策略的比较进一步验证了优化路由策略的优异性能. 关键词： 优化路由策略 复杂网络 负载传输 网络阻塞     

Topological probability and connection strength induced activity in complex neural networks

Recent experimental evidence suggests that some brain activities can be assigned to small-world networks. In this work, we investigate how the topological probability p and connection strength C affect the activities of discrete neural networks with small-world (SW) connections. Network elements are described by two-dimensional map neurons (2DMNs) with the values of parameters at which no activity occurs. It is found that when the value of p is smaller or larger, there are no active neurons in the network, no matter what the value of connection strength is; for a given appropriate connection strength, there is an intermediate range of topological probability where the activity of 2DMN network is induced and enhanced. On the other hand, for a given intermediate topological probability level, there exists an optimal value of connection strength such that the frequency of activity reaches its maximum. The possible mechanism behind the action of topological probability and connection strength is addressed based on the bifurcation method. Furthermore, the effects of noise and transmission delay on the activity of neural network are also studied.     

Optimization-based topology identification of complex networks

In many cases, the topological structures of a complex network are unknown or uncertain, and it is of significance to identify the exact topological structure. An optimization-based method of identifying the topological structure of a complex network is proposed in this paper. Identification of the exact network topological structure is converted into a minimal optimization problem by using the estimated network. Then, an improved quantum-behaved particle swarm optimization algorithm is used to solve the optimization problem. Compared with the previous adaptive synchronization-based method, the proposed method is simple and effective and is particularly valid to identify the topological structure of synchronization complex networks. In some cases where the states of a complex network are only partially observable, the exact topological structure of a network can also be identified by using the proposed method. Finally, numerical simulations are provided to show the effectiveness of the proposed method.     

On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators

We study synchrony optimized networks. In particular, we focus on the Kuramoto model with non-identical native frequencies on a random graph. In a first step, we generate synchrony optimized networks using a dynamic breeding algorithm, whereby an initial network is successively rewired toward increased synchronization. These networks are characterized by a large anti-correlation between neighbouring frequencies. In a second step, the central part of our paper, we show that synchrony optimized networks can be generated much more cost efficiently by minimization of an energy-like quantity E and subsequent random rewires to control the average path length. We demonstrate that synchrony optimized networks are characterized by a balance between two opposing structural properties: A large number of links between positive and negative frequencies of equal magnitude and a small average path length. Remarkably, these networks show the same synchronization behaviour as those networks generated by the dynamic rewiring process. Interestingly, synchrony-optimized network also exhibit significantly enhanced synchronization behaviour for weak coupling, below the onset of global synchronization, with linear growth of the order parameter with increasing coupling strength. We identify the underlying dynamical and topological structures, which give rise to this atypical local synchronization, and provide a simple analytical argument for its explanation.     

基于复杂网络理论的北京公交网络拓扑性质分析

为分析公交复杂网络的拓扑性质, 本文以北京市为例, 选取截止到2010年7月的北京全市(14区、2县)的1165条公交线路和9618个公交站点为样本数据, 运用复杂网络理论构建起基于邻接站点的有向加权复杂网络模型. 该方法以公交站点作为节点, 相邻站点之间的公交线路作为边, 使得网络既具有复杂网络的拓扑性质同时节点(站点)又具有明确的地理坐标. 对网络中节点度、点强度、强度分布、平均最短路径、聚类系数等性质的分析显示, 公交复杂网络的度和点强度分布极为不均, 网络中前5%和前10%节点的累计强度分布分别达到22.43%和43.02%; 点强度与排列序数、累积强度分布都服从幂律分布, 具有无标度和小世界的网络特点, 少数关键节点在网络中发挥着重要的连接作用. 为分析复杂网络中的关键节点, 本文通过承载压力分析和基于"掠夺" 的区域中心节点提取两种方法, 得到了公交复杂网络中两类不同表现的关键节点. 这些规律也为优化城市公交网络及交通规划发展提供了新的参考建议.     

Epidemic Spread in Networks Induced by Deactivation Mechanism

We have studied the topology and epidemic spreading behaviors on the networks in which deactivation mechanism and long-rang connection are coexisted. By means of numerical simulation, we find that the clustering coefficient C and the Pearson correlation coefficient r decrease with increasing long-range connection μ and the topological state of the network changes into that of BA model at the end （when μ = 1）. For the Susceptible-Infect-Susceptible model of epidemics, the epidemic threshold can reach maximum value at μ = 0.4 and presents two different variable states around μ= 0.4.     

基于复杂网络理论的微博用户关系网络演化模型研究

微博给人们提供便利的同时也产生了较大的负面影响.为获取微博谣言的传播规律,进而采取有效措施防控其传播,本文基于复杂网络理论研究微博用户关系网络的内部特征,提出一种微博用户关系网络演化模型,借助于平均场理论,分析该演化模型的拓扑统计特性,以及谣言在该演化模型上的传播动力学行为.理论分析和仿真实验表明,由该模型演化生成的微博用户关系网络具有无标度特性.度分布指数不仅与反向连接概率有关,而且还取决于节点的吸引度分布.研究还发现,与指数分布和均匀分布相比,当节点吸引度满足幂律分布时,稳态时的谣言传播程度较大.此外,随着反向连接概率或节点初始连边数量的增加,谣言爆发的概率以及网络中最终接受谣言的节点数量都会明显增大.     

磁刺激穴位复杂脑功能网络构建与分析

本文采用互信息方法对磁刺激内关穴过程中的脑电信 号进行了两两通道间非线性时域关联特性分析, 构建了不同频率刺激前、刺激中、刺激后的脑功能网络, 并基于复杂网络理论对脑功能网络的特征进行了深入研究. 结果表明, 磁刺激频率为3 Hz 时, 大脑功能网络的平均度、平均聚类系数和全局效率与刺激前相比均有显著升高, 平均路径长度显著降低, 并且相应脑功能网络的"小世界"属性有所增强, 信息在大脑各区域间的传递更加高效. 本研究首次开展了磁刺激穴位复杂脑功能网络的构建与分析, 为探索磁刺激穴位对大脑神经调节的作用和机理提供新思路和新方法. 关键词： 复杂网络 磁刺激 脑功能网络 互信息     

An estimation formula for the average path length of scale-free networks

A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, $N$, as the only parameter, two parameters including $N$ and a second parameter $\alpha $ are included in our formula. The parameter $\alpha $ is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.