识别高阶网络传播中最有影响力的节点

识别网络传播中最有影响力的节点是控制传播速度和范围的重要步骤,有助于加速有益信息扩散,抑制流行病、谣言和虚假信息的传播等.已有研究主要基于描述点对交互的低阶复杂网络.然而,现实中个体间的交互不仅发生在点对之间,也发生在3个及以上节点形成的群体中.群体交互可利用高阶网络来刻画,如单纯复形与超图.本文研究单纯复形上最有影响力的传播者识别方法.首先,提出单纯复形上易感-感染-恢复(SIR)微观马尔可夫链方程组,定量刻画单纯复形上的疾病传播动力学.接下来利用微观马尔可夫链方程组计算传播动力学中节点被感染的概率.基于网络结构与传播过程,定义节点的传播中心性,用于排序节点传播影响力.在两类合成单纯复形与4个真实单纯复形上的仿真结果表明,相比于现有高阶网络中心性和复杂网络中最优的中心性指标,本文提出的传播中心性能更准确地识别高阶网络中最有影响力的传播者.     

基于在线社交网络的信息传播模型

本文构造了一个基于在线社交网络的信息传播模型.该模型考虑了节点度和传播机理的影响,结合复杂网络和传染病动力学理论,进一步建立了动力学演化方程组.该方程组刻画了不同类型节点随着时间的演化关系,反映了传播动力学过程受到网络拓扑结构和传播机理的影响.本文模拟了在线社交网络中的信息传播过程,并分析了不同类型节点在网络中的行为规律.仿真结果表明:由于在线社交网络的高度连通性,信息在网络中传播的门槛几乎为零;初始传播节点的度越大,信息越容易在网络中迅速传播;中心节点具有较大的社会影响力;具有不同度数的节点在网络中的变 关键词： 在线社交网络 信息传播 微分方程 传染病动力学     

复杂网络中最小K-核节点的传播能力分析

K-核分解方法对于识别复杂网络传播动力学中最重要节点具有重要的价值, 然而该方法无法对复杂网络中大量最小K-核节点的传播能力进行准确度量. 本文主要考察最小K-核节点的传播行为, 利用其邻居的K-核信息, 提出一种度量这类节点传播能力的方法. 实证网络数据集的传播行为仿真结果表明, 该方法与度、介数等指标相比更能准确度量最小K-核节点的传播能力. 关键词： 复杂网络 传播能力 K-核分解 最小K-核节点     

微博双向“关注”网络节点中心性及传播 影响力的分析

根据新浪微博的实际数据, 建立了两个基于双向“关注”的用户关系网络, 通过分析网络拓扑统计特征, 发现二者均具有小世界、无标度特征. 通过对节点度、紧密度、介数和k-core 四个网络中心性指标进行实证分析, 发现节点度服从分段幂率分布; 介数相比其他中心性指标差异性最为显著; 两个网络均具有明显的层次性, 但不是所有度值大的节点核数也大; 全局范围内各中心性指标之间存在着较强的相关性, 但在度值较大的节点群这种相关性明显减弱. 此外, 借助基于传染病动力学的SIR信息传播模型来分析四种指标在刻画节点传播能力方面的差异性, 仿真结果表明, 选择具有不同中心性指标的初始传播节点, 对信息传播速度和范围均具有不同影响; 紧密度和k-core较其他指标可以更加准确地描述节点在信息传播中所处的网络核心位置, 这有助于识别信息传播拓扑网络中的关键节点.     

基于时间序列的网络失效模型

随着网络科学的发展,静态网络已不能清晰刻画网络的动态过程.在现实网络中,个体之间的交互随时间而快速演化.这种网络模式将时间与交互过程紧密联系,能够清晰刻画节点的动态过程.因此,如何更好地基于时间序列刻画网络行为变化是现有级联失效研究的重要问题.为了更好地研究该问题,本文提出一种基于时间序列的失效模型.通过随机攻击某时刻的节点,分析了时间、激活比例、连边数、连接概率4个参数对失效的影响并发现网络相变现象.同时为验证该模型的有效性与科学性,采用真实网络进行研究.实验表明,该模型兼顾时序以及传播动力学,具有较好的可行性,为解释现实动态网络的级联传播提供了参考.     

基于有向渗流理论的关联微博转发网络信息传播研究

微博网络的快速性、爆发性和时效性, 以及用户复杂的行为模式, 使得研究其信息传播模型及影响因素成为网络舆情的热点方向. 利用压缩映射定理, 分析不动点迭代过程的收敛条件, 得到有向网络信息传播过程的渗流阈值和巨出向分支的数值解法; 通过可变同配系数生成模型, 分析关联特征对信息传播的影响; 最后利用微博转发网络数据进行仿真对比实验. 结果表明: 虽然四类关联特征同时体现出同配、异配特征, 但信息传播结果更多受入度-入度相关性、入度-出度相关性影响; 通过删除少量节点的方法, 提取边同配比例, 验证大部分节点的四类关联特征呈现一致性.     

多关系网络上的流行病传播动力学研究

多关系网络已经吸引了许多人的注意, 目前的研究主要涉及其拓扑结构及其演化的分析、 不同类型关系的挖掘、重叠社区的检测、级联失效动力学等. 然而,多关系网络上流行病传播的研究还相对较少. 由此提出一种双关系网络模型(工作-朋友关系网), 研究多关系对于流行病传播动力学行为的影响. 在全接触模式下, 多关系的存在会显著降低网络中的爆发阈值, 使得疾病更容易流行而难以控制. 对比ER (Erdös-Rènyi), WS (Watts-Strogatz), BA (Barabási-Albert)三种网络, 由于结构异质性的差异, WS网络受到的影响最大, ER网络次之, BA网络最小. 有趣的是, 其爆发阈值的相对变化大小与网络结构无关. 在单点接触模式下, 增加强关系的权重将显著提升爆发阈值, 降低感染密度; 随着强关系的比例变化将出现最优值现象: 极大的爆发阈值和极小的感染密度. 随着强关系的边权增加, 达到最优值的边比例将减少. 更为有趣的是, 三个网络中优值出现的位置几乎一致, 独立于网络结构. 这一研究不但有助于理解多关系网络上的病毒传播过程, 也为多关系网络研究提供了一个新的视角. 关键词： 多关系网络 流行病传播 接触模式 爆发阈值     

一种信息传播促进网络增长的网络演化模型

为了研究信息传播过程对复杂网络结构演化的影响,提出了一种信息传播促进网络增长的网络演化模型,模型包括信息传播促进网内增边、新节点通过局域世界建立第一条边和信息传播促进新节点连边三个阶段,通过多次自回避随机游走模拟信息传播过程,节点根据路径节点的节点度和距离与其选择性建立连接。理论分析和仿真实验表明,模型不仅具有小世界和无标度特性,而且不同参数下具有漂移幂律分布、广延指数分布等分布特性,呈现小变量饱和、指数截断等非幂律现象,同时,模型可在不改变度分布的情况下调节集聚系数,并能够产生从同配到异配具有不同匹配模式的网络.     

基于多阶邻居壳数的向量中心性度量方法

K-壳分解法在度量复杂网络中节点的重要性方面具有重要的理论意义和应用价值.但K-壳方法中,存在大量壳值相等的节点,从而无法精确地比较这些具有相同壳值节点的相对重要性.因此,本文基于网络中节点自身壳值与其多阶邻居的壳值,设计利用向量的形式来表示节点在复杂网络中的相对重要性程度,提出了多阶邻居壳数向量中心性方法,并设计了该中心性向量比较方法.通过在七个真实网络中进行消息传播与静态攻击实验,发现基于多阶邻居壳数向量的中心性方法具有计算复杂度低,能够有效发现具有高传播能力的节点,在传播实验中具有优越的性能.并在静态攻击实验过程中倾向于优先破坏网络中的传播核心结构.多阶邻居壳数向量中心性方法在保留K-壳中心性信息的前提下,极大提高了节点重要性的区别程度,平衡了对节点在复杂网络中联通结构的重要性的度量和对传播结构重要性的度量,因此具有重要理论意义与应用价值.     

处理NaCs光解离问题的两种方案比较

利用含时波包动力学方法中的劈裂算符-傅里叶变换传播方案和切比雪夫多项式展开方案研究了Na Cs分子的光吸收截面,并对由这两种方案计算得出的结果进行了比较.结果表明劈裂算符-傅立叶变换传播方案能更好地展示光吸收截面的中间动力学信息,而在研究初始波包与光吸收截面的关系时,由切比雪夫多项式展开方案获得的结果则更直观.利用后一方案计算的从基态X1∑+不同振动态跃迁到激发态B1∑+上相应的光吸收截面的结果表明,初始波包对光吸收截面有一定的影响,所有振动态的吸收截面均表现出谐振行为,即每一个振动态吸收截面最小值的个数恰好等于基态振动态波函数节点的个数,这种节点映射行为与映射原理相符合.     

The importance of centralities in dark network value chains

This paper introduces three novel centrality measures based on the nodes’ role in the operation of a joint task, i.e., their position in a criminal network value chain. For this, we consider networks where nodes have attributes describing their “capabilities” or “colors”, i.e., the possible roles they may play in a value chain. A value chain here is understood as a series of tasks to be performed in a specific order, each requiring a specific capability. The first centrality notion measures how many value chain instances a given node participates in. The other two assess the costs of replacing a node in the value chain in case the given node is no longer available to perform the task. The first of them considers the direct distance (shortest path length) between the node in question and its nearest replacement, while the second evaluates the actual replacement process, assuming that preceding and following nodes in the network should each be able to find and contact the replacement. In this report, we demonstrate the properties of the new centrality measures using a few toy examples and compare them to classic centralities, such as betweenness, closeness and degree centrality. We also apply the new measures to randomly colored empirical networks. We find that the newly introduced centralities differ sufficiently from the classic measures, pointing towards different aspects of the network. Our results also pinpoint the difference between having a replacement node in the network and being able to find one. This is the reason why “introduction distance” often has a noticeable correlation with betweenness. Our studies show that projecting value chains over networks may significantly alter the nodes’ perceived importance. These insights might have important implications for the way law enforcement or intelligence agencies look at the effectiveness of dark network disruption strategies over time.     

Computing Influential Nodes Using the Nearest Neighborhood Trust Value and PageRank in Complex Networks

Computing influential nodes gets a lot of attention from many researchers for information spreading in complex networks. It has vast applications, such as viral marketing, social leader creation, rumor control, and opinion monitoring. The information-spreading ability of influential nodes is greater compared with other nodes in the network. Several researchers proposed centrality measures to compute the influential nodes in a complex network, such as degree, betweenness, closeness, semi-local centralities, and PageRank. These centrality methods are defined based on the local and/or global information of nodes in the network. However, due to their high time complexity, centrality measures based on the global information of nodes have become unsuitable for large-scale networks. Very few centrality measures exist that are based on the attributes between nodes and the structure of the network. We propose the nearest neighborhood trust PageRank (NTPR) based on the structural attributes of neighbors and nearest neighbors of nodes. We define the measure based on the degree ratio, the similarity between nodes, the trust values of neighbors, and the nearest neighbors. We computed the influential nodes in various real-world networks using the proposed centrality method. We found the maximum influence by using influential nodes with SIR and independent cascade methods. We also compare the maximum influence of our centrality measure with the existing basic centrality measures.     

Rethinking failure and attack tolerance assessment in complex networks

Studies have revealed that real complex networks are inherently vulnerable to the loss of high centrality nodes. These nodes are crucial to maintaining the network connectivity and are identified by classical measures, such as degree and betweenness centralities. Despite its significance, an assessment based solely on this vulnerability premise is misleading for the interpretation of the real state of the network concerning connectivity. As a matter of fact, some networks may be in a state of imminent fragmentation before such a condition is fully characterized by an analysis targeted solely on the centrally positioned nodes. This work aims at showing that, in fact, it is basically the global network configuration that is responsible for network fragmentation, as it may allow many other lower centrality nodes to seriously damage the network connectivity.     

Centrality measure of complex networks using biased random walks

We propose a novel centrality measure based on the dynamical properties of a biased random walk to provide a general framework for the centrality of vertex and edge in scale-free networks (SFNs). The suggested centrality unifies various centralities such as betweenness centrality (BC), load centrality (LC) and random walk centrality (RWC) when the degree, k, is relatively large. The relation between our centrality and other centralities in SFNs is clearly shown by both analytic and numerical methods. Regarding to the edge centrality, there have been few established studies in complex networks. Thus, we also provide a systematic analysis for the edge BC (LC) in SFNs and show that the distribution of edge BC satisfies a power-law. Furthermore we also show that the suggested centrality measures on real networks work very well as on the SFNs.     

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.     

The spreading of opposite opinions on online social networks with authoritative nodes

The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites.     

Optimal navigation for characterizing the role of the nodes in complex networks

In this paper, we explore how the approach of optimal navigation (Cajueiro (2009) [33]) can be used to evaluate the centrality of a node and to characterize its role in a network. Using the subway network of Boston and the London rapid transit rail as proxies for complex networks, we show that the centrality measures inherited from the approach of optimal navigation may be considered if one desires to evaluate the centrality of the nodes using other pieces of information beyond the geometric properties of the network. Furthermore, evaluating the correlations between these inherited measures and classical measures of centralities such as the degree of a node and the characteristic path length of a node, we have found two classes of results. While for the London rapid transit rail, these inherited measures can be easily explained by these classical measures of centrality, for the Boston underground transportation system we have found nontrivial results.     

基于扩展度的复杂网络传播影响力评估算法

对网络中节点的传播影响力进行评估具有十分重要的意义, 有助于促进有益或抑制有害信息的传播. 目前, 多种中心性指标可用于对节点的传播影响力进行评估, 然而它们一般只有当传播率处于特定范围时才能取得理想的结果. 例如, 度值中心性指标在传播率较小时较为合适, 而半局部中心性和接近中心性指标则适用于稍大一些的传播率. 为了解决各种评估指标对传播率敏感的问题, 提出了一种基于扩展度的传播影响力评估算法. 算法利用邻居节点度值叠加的方式对节点度的覆盖范围进行了扩展, 使不同的扩展层次对应于不同的传播率, 并通过抽样测试确定了适合于特定传播率的层次数. 真实和模拟数据集上的实验结果表明, 通过扩展度算法得到的扩展度指标能在不同传播率下对节点的传播影响力进行有效评估, 其准确性能够达到或优于利用其他中心性指标进行评估的结果.     

The relative importance of structure and dynamics on node influence in reversible spreading processes

The reversible spreading processes with repeated infection widely exist in nature and human society, such as gonorrhea propagation and meme spreading. Identifying influential spreaders is an important issue in the reversible spreading dynamics on complex networks, which has been given much attention. Except for structural centrality, the nodes’ dynamical states play a significant role in their spreading influence in the reversible spreading processes. By integrating the number of outgoing edges and infection risks of node’s neighbors into structural centrality, a new measure for identifying influential spreaders is articulated which considers the relative importance of structure and dynamics on node influence. The number of outgoing edges and infection risks of neighbors represent the positive effect of the local structural characteristic and the negative effect of the dynamical states of nodes in identifying influential spreaders, respectively. We find that an appropriate combination of these two characteristics can greatly improve the accuracy of the proposed measure in identifying the most influential spreaders. Notably, compared with the positive effect of the local structural characteristic, slightly weakening the negative effect of dynamical states of nodes can make the proposed measure play the best performance. Quantitatively understanding the relative importance of structure and dynamics on node influence provides a significant insight into identifying influential nodes in the reversible spreading processes.