复杂网络中节点重要性排序的研究进展

如何用定量分析的方法识别超大规模网络中哪些节点最重要, 或者评价某个节点相对于其他一个或多个节点的重要程度, 这是复杂网络研究中亟待解决的重要问题之一. 本文分别从网络结构和传播动力学的角度, 对现有的复杂网络中节点重要性排序方法进行了系统的回顾,总结了节点重要性排序方法的最新研究进展, 并对不同的节点重要性排序指标的优缺点以及适用环境进行了分析, 最后指出了这一领域中几个有待解决的问题及可能的发展方向. 关键词： 复杂网络 节点重要性 网络结构 传播动力学     

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小...     

一种新的模糊多属性群决策方法

现有模糊多属性群决策方法大都没有考虑决策者的权重，更没有考虑决策者评价的一致性程度对群体评价结果的影响。提出的模糊多属性群决策方法将同时考虑这两方面的因素，以使决策方法及决策结果更符合客观实际。     

基于区域密度曲线识别网络上的多影响力节点

复杂网络多影响力节点的识别可以帮助理解网络的结构和功能,具有重要的理论意义和应用价值.本文提出一种基于网络区域密度曲线的多影响力节点的识别方法.应用两种不同的传播模型,在不同网络上与其他中心性指标进行了比较.结果表明,基于区域密度曲线的识别方法能够更好地识别网络中的多影响力节点,选中的影响力节点之间的分布较为分散,自身也比较重要.本文所提方法是基于网络的局部信息,计算的时间复杂度较低.     

基于度与集聚系数的网络节点重要性度量方法研究

网络中节点重要性度量对于研究网络的鲁棒性具有十分重要的意义. 研究者们普遍运用度或集聚系数来度量节点的重要程度, 然而度指标只考虑节点自身邻居个数而忽略了其邻居之间的信息, 集聚系数只考虑节点邻居之间的紧密程度而忽略了其邻居的规模. 本文综合考虑节点的邻居个数, 以及其邻居之间的连接紧密程度, 提出了一种基于邻居信息与集聚系数的节点重要性评价方法. 对美国航空网络和美国西部电力网进行的选择性攻击实验表明, 采用该方法的效果较k-shell指标可以分别提高24%和112%. 本文的节点重要性度量方法只需要考虑网络局部信息, 因此非常适合于对大规模网络的节点重要性进行有效分析. 关键词： 网络科学 鲁棒性 节点重要性 集聚系数     

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.     

基于联合矩阵分解的节点多属性网络社团检测

发现复杂网络中的社团结构在社会网络、生物组织网络和在线网络等复杂网络中具备十分重要的意义. 针对社交媒体网络的社团检测通常需要利用两种信息源: 网络拓扑结构特征和节点属性特征, 丰富的节点内容属性信息为社团检测的增加了灵活性和挑战. 传统方法是要么仅针对这两者信息之一进行单独挖掘, 或者将两者信息得到的社团结果进行线性叠加判决, 不能有效进行信息源的融合. 本文将节点的多维属性特征作为社团划分的一种有效协同学习项进行研究, 将两者信息源进行融合分析, 提出了一种基于联合矩阵分解的节点多属性网络社团检测算法CDJMF, 提高了社团检测的有效性和鲁棒性. 实验表明, 本文所提的方法能够有效利用节点的属性信息指导社团检测, 具备更高的社团划分质量.     

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.     

模拟复杂网络下子网络节点抗攻击设计

针对复杂网络节点受攻击而出现的安全性问题,提出在模拟复杂网络基础上结合Feistel算法的子网络节点抵抗攻击方法。该方法通过子网络节点定位参数集,建立恶意节点位置模型,并确定定位真实精度;而后利用Feistel算法对节点密文进行加密处理,进而使加密信息恢复成明文信息,完成模拟复杂网络下子网络节点的抗攻击方法改进。结果证明,该方法不仅能够准确的对恶意节点进行定位,而且增强了节点抗攻击性能,提升了网络安全性。     

具有随机节点结构的复杂网络同步研究

针对具有随机节点结构的复杂网络, 研究其同步问题. 基于Lyapunov稳定性理论和线性矩阵不等式技术给出了复杂网络同步稳定的充分性条件, 该充分性条件不仅与复杂网络的状态时延有关, 还与节点结构的概率分布有关. 数值仿真表明本文方法的有效性. 关键词： 复杂网络 随机节点 同步稳定 时滞     

叶子节点对于网络同步能力影响的研究

系统考察了叶子节点对于网络同步能力的影响,发现随着叶子节点比例的增加,网络的同步能力下降,同时给出了数值结果以及理论解释. 关键词： 复杂网络 叶子节点 同步能力     

Identifying influential nodes in complex networks

Identifying influential nodes that lead to faster and wider spreading in complex networks is of theoretical and practical significance. The degree centrality method is very simple but of little relevance. Global metrics such as betweenness centrality and closeness centrality can better identify influential nodes, but are incapable to be applied in large-scale networks due to the computational complexity. In order to design an effective ranking method, we proposed a semi-local centrality measure as a tradeoff between the low-relevant degree centrality and other time-consuming measures. We use the Susceptible-Infected-Recovered (SIR) model to evaluate the performance by using the spreading rate and the number of infected nodes. Simulations on four real networks show that our method can well identify influential nodes.     

Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes

In this paper, we investigate the impulsive synchronization between two coupled complex networks with time-delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat's lemma, the global asymptotic impulsive synchronization of the drive—response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.     

面向结构洞的复杂网络关键节点排序

复杂网络中的结构洞节点对于信息传播具有重要作用, 现有关键节点排序方法多数没有兼顾结构洞节点和其他类型的关键节点进行排序. 本文根据结构洞理论与关键节点排序相关研究选取了网络约束系数、介数中心性、等级度、效率、网络规模、PageRank值以及聚类系数7个度量指标, 将基于ListNet的排序学习方法引入到复杂网络的关键节点排序问题中, 融合7个度量指标, 构建了一个能够综合评价面向结构洞节点的关键节点排序方法. 采用模拟网络和实际复杂网络进行了大量实验, 人工标准试验结果表明本文排序方法能够综合考虑结构洞节点和核心节点, 关键节点排序与人工排序结果具有较高的一致性. SIR传播模型评估实验结果表明由本文选择TOP-K节点发起的传播能够在较短的传播时间内达到最大的传播范围.     

Identifying all-around nodes for spreading dynamics in complex networks

Identifying the most influential nodes in complex networks provides a strong basis for understanding spreading dynamics and ensuring more efficient spread of information. Due to the heterogeneous degree distribution, we observe that current centrality measures are correlated in their results of nodes ranking. This paper introduces the concept of all-around nodes, which act like all-around players with good performance in combined metrics. Then, an all-around distance is presented for quantifying the influence of nodes. The experimental results of susceptible-infectious-recovered (SIR) dynamics suggest that the proposed all-around distance can act as a more accurate, stable indicator of influential nodes.     

Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence(IS) to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.     

LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks

Identifying influential nodes in complex networks is one of the most significant and challenging issues, which may contribute to optimizing the network structure, controlling the process of epidemic spreading and accelerating information diffusion. The node importance ranking measures based on global information are not suitable for large-scale networks due to their high computational complexity. Moreover, they do not take into account the impact of network topology evolution over time, resulting in limitations in some applications. Based on local information of networks, a local clustering H-index (LCH) centrality measure is proposed, which considers neighborhood topology, the quantity and quality of neighbor nodes simultaneously. The proposed measure only needs the information of first-order and second-order neighbor nodes of networks, thus it has nearly linear time complexity and can be applicable to large-scale networks. In order to test the proposed measure, we adopt the susceptible-infected-recovered (SIR) and susceptible-infected (SI) models to simulate the spreading process. A series of experimental results on eight real-world networks illustrate that the proposed LCH can identify and rank influential nodes more accurately than several classical and state-of-the-art measures.     

Oscillation sources and wave propagation paths in complex networks consisting of excitable nodes

Self-sustained oscillations in complex networks consisting of nonoscillatory nodes have attracted long-standing interest in diverse natural and social systems. We study the self-sustained periodic oscillations in random networks consisting of excitable nodes. We reveal the underlying dynamic structure by applying a dominant phase-advanced driving method. The oscillation sources and wave propagation paths can be illustrated clearly via the dynamic structure revealed. Then we are able to control the oscillations with surprisingly high efficiency based on our understanding.