节点抗攻击存在差异的无尺度网络恶意软件传播研究

在考虑节点抗攻击能力存在差异情形下,研究了恶意软件在无尺度网络中的传播行为.基于元胞自动机理论,建立了节点具有攻击差异的恶意软件传播模型.通过定义脆弱性函数,以描述不同度节点的抗攻击差异,使得模型更具普遍性.研究了不同形式的脆弱性函数对恶意软件在无尺度网络中的传播临界值和时间演化的影响.研究表明,节点抗攻击能力的差异对传播行为会产生重要影响,如导致传播临界值改变、传播速度减缓.研究指出,脆弱性函数是网络选择适合的免疫策略的重要依据.     

复杂网络中考虑不完全免疫的病毒传播研究

复杂网络中不完全免疫包括免疫失败和免疫失效两种情况,本文研究两者同时存在对网络病毒传播行为的影响,基于平均场理论,提出一种新的传播模型.理论分析表明,免疫失败和免疫失效同时存在显著降低了网络的传播临界值,增强了病毒的感染程度.根据传播临界值与免疫节点密度、免疫成功率以及免疫失效率之间的关系,给出有效控制网络病毒传播的策略.通过数值仿真进行验证。     

无标度网络中最大传染能力限定的病毒传播问题研究

传统的病毒传播模型在无限大无标度网络上不存在病毒传播阈值,即无论病毒的传播速率多么低,病毒始终能够在网络中传播.但研究发现,这个结论是在网络中存在超级传染者的假设下得到的,然而许多真实的无标度网络中并不存在超级传染者.因此,文章提出了一个最大传染能力限定的病毒传播模型,并从理论上证明了在最大传染能力限定的无限大无标度网络上,病毒传播阈值是存在的;同时,也分析了最大传染能力限定下非零传播阈值与有限规模网络下非零传播阈值的本质区别,并解释了为什么人们总是认为传统病毒传播模型对许多真实网络病毒感染程度估计过高的 关键词： 无标度网络 最大传染能力 传播阈值 感染程度     

具有跨邻居传播能力的信息辐射模型研究

针对大多数信息传播的研究均只考虑邻居的问题,本文提出了一个具有跨邻居传播能力的信息辐射模型.该模型结合复杂网络理论、平均场理论和辐射理论,建立了以物理层为网络结构基础、以辐射层为信息传播环境、以状态层为辐射状态统计的三层信息辐射网络模型.通过定义节点状态之间的转换规则和相关网络统计量,引入辐射范围和辐射衰减量,分析了辐射机理并推导了辐射阈值表达式.在不同的复杂网络中,利用数值仿真验证了理论分析的正确性和模型的有效性,分析了节点之间的状态转换概率和辐射衰减量对信息辐射的影响规律.     

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.     

考虑网络流量的无标度网络病毒免疫策略研究

考虑网络交通流量对病毒传播行为的影响,基于平均场理论研究无标度网络上的病毒免疫策略,提出一种改进的熟人免疫机理.理论分析表明,在考虑网络交通流量影响的情况下,当免疫节点密度较小时,随机免疫几乎不能降低病毒的传播速率,而对网络实施目标免疫则能够有效抑制病毒的传播,并且选择度最大的节点进行免疫与选择介数最大的节点进行免疫的效果基本相同.研究还发现,对于网络全局信息未知的情况,与经典熟人免疫策略相比,所提出的免疫策略能够获得更好的免疫效果.通过数值仿真对理论分析进行了验证. 关键词： 无标度网络 病毒传播 交通流量 免疫策略     

基于元胞自动机考虑传播延迟的复杂网络病毒传播研究

基于元胞自动机,研究传播延迟对复杂网络病毒传播动力学行为的影响,提出一种新的易染状态-感染状态-易染状态(SIS)传播模型.研究表明,传播延迟的存在显著降低了网络的传播临界值,增强了网络中病毒爆发的危险性.研究还发现,随着传播延迟的增大,病毒的感染程度以及传播速率都明显增大.此外,SIS传播模型不仅能够反映病毒的平均传播趋势,而且可以描述病毒随时间的动态演化过程以及病毒的爆发和消亡等概率事件,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒平均传播趋势的局限性.同时,还给出有效控制网络中病毒传 关键词： 复杂网络 病毒传播 元胞自动机 传播延迟     

一种基于用户相对权重的在线社交网络信息传播模型

根据在线社交网络信息传播特点和目前社交网络传播模型研究中存在的问题, 本文定义了网络用户之间的相互影响力函数, 在此基础上提出了一种基于用户相对权重的社交网络信息传播模型, 并对网络中的传播路径及传播过程进行了分析, 讨论了不同路径的信息传播影响力.为验证模型的有效性, 将传统的SIR模型和本文模型在六类不同网络拓扑下进行了仿真实验.仿真结果表明, 两类模型在均匀网络中没有明显差异, 但在非均匀网络中本文模型更能体现真实网络特点, 实验同时验证了节点的地位影响着信息的传播, 并且发现英文社交平台Twitter和中文社交平台新浪微博在拓扑结构上具备一定相似性.     

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.     

一种简化非Gauss场模型在随机介质中光传播问题中的应用

为了研究大气湍流间歇性的光传播效应，构造出一种比较简单的非Gauss场模型(Poission场 )用于描述大气介电常数(或折射率)随机起伏.模型特征泛函含有四个待定函数，根据大气湍 流的统计均匀性，介电起伏的单点概率分布函数，以及介电起伏能谱可以选择或确定它们. 对在这种简化湍流中传播的光波平均场及二阶统计矩性质进行了理论分析，并给出数值模拟 的一个简单例子. 关键词： 光波传播 大气湍流 间歇性     

Disease spreading on fitness-rewired complex networks

As people travel, human contact networks may change topologically from time to time. In this paper, we study the problem of epidemic spreading on this kind of dynamic network, specifically the one in which the rewiring dynamics of edges are carried out to preserve the degree of each node (called fitness rewiring). We also consider the adaptive rewiring of edges, which encourages disconnections from and discourages connections to infected nodes and eventually leads to the isolation of the infected from the susceptible with only a small number of links between them. We find that while the threshold of epidemic spreading remains unchanged and prevalence increases in the fitness rewiring dynamics, meeting of the epidemic threshold is delayed and prevalence is reduced (if adaptive dynamics are included). To understand these different behaviors, we introduce a new measure called the “mean change of effective links” and find that creation and deletion of pathways for pathogen transmission are the dominant factors in fitness and adaptive rewiring dynamics, respectively.     

具有局部结构的增长无标度网络中传染病传播机制研究

为了研究人群中的一些基本的社会关系结构,如家庭、室友、同事等,对传染病传播过程的影响机制,本文建立了一个具有局部结构的增长无标度网络模型.研究表明,局部结构的引入使得该网络模型能够同时再现社会网络的两个重要特征：节点度分布的不均匀性以及节点度之间的相关性.首先,该网络的节点度和局部结构度均服从幂律分布,且度分布指数依赖于局部结构的大小.此外,局部结构的存在还导致网络节点度之间具有正相关特性,而这种正相关正是社会网络所特有的一个重要特性.接着,通过理论分析和数值模拟,我们进一步研究了该网络结构对易感者-感染 关键词： 复杂网络 无标度网络 局部结构 传染病建模     

A Weighted Configuration Model and Inhomogeneous Epidemics

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting how closely ‘connected’ the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that R ₀ can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.     

Epidemic threshold and immunization on generalized networks

The susceptible–infected–susceptible (SIS) model is widely adopted in the studies of epidemic dynamics. When it is applied on contact networks, these networks mostly consist of nodes connected by undirected and unweighted edges following certain statistical properties, whereas in this article we consider the threshold and immunization problem for the SIS model on generalized networks that may contain different kinds of nodes and edges which are very possible in the real situation. We proved that an epidemic will become extinct if and only if the spectral radius of the corresponding parameterized adjacent matrix (PAM) is smaller than 1. Based on this result, we can evaluate the efficiency of immune strategies and take several prevailing ones as examples. In addition, we also develop methods that can precisely find the optimal immune strategies for networks with the given PAM.     

Statistical model for the effects of phase and momentum randomization on electron transport

In this paper, the study of epidemic spreading of mobile individuals on networks focuses on the system in which each node of the network may be occupied by either one individual or a void, and each individual could move to a neighbour void node. It is found that for the susceptible-infected-susceptible (SIS) model, the diffusion increases the epidemic threshold for arbitrary heterogeneous networks having the degree fluctuations, and the diffusion doesn??t affect the epidemic threshold for regular random networks. In the SI model, the diffusion suppresses the epidemic spread at the early outbreak stage, which indicates that the growth time scale of outbreaks is monotonically increasing with diffusion rate d. The heterogeneous mean-field analysis is in good agreement with the numerical simulations on annealed networks.     

Effect of node deleting on network structure

The ever-increasing knowledge of the structure of various real-world networks has uncovered their complex multi-mechanism-governed evolution processes. Therefore, a better understanding of the structure and evolution of these networked complex systems requires us to describe such processes in a more detailed and realistic manner. In this paper, we introduce a new type of network growth rule which comprises addition and deletion of nodes, and propose an evolving network model to investigate the effect of node deleting on network structure. It is found that, with the introduction of node deleting, network structure is significantly transformed. In particular, degree distribution of the network undergoes a transition from scale-free to exponential forms as the intensity of node deleting increases. At the same time, nontrivial disassortative degree correlation develops spontaneously as a natural result of network evolution in the model. We also demonstrate that node deleting introduced in the model does not destroy the connectedness of a growing network so long as the increasing rate of edges is not excessively small. In addition, it is found that node deleting will weaken but not eliminate the small-world effect of a growing network, and generally it will decrease the clustering coefficient in a network.     

Epidemic centrality — is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as “superspreaders”, are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed.     

一种改进的基于信息传播率的复杂网络影响力评估算法

评价网络中节点的信息传播影响力对于理解网络结构与网络功能具有重要意义.目前,许多基于最短路径的指标,如接近中心性、介数中心性以及半局部(SP)指标等相继用于评价节点传播影响力.最短路径表示节点间信息传播途径始终选择最优方式,然而实际上网络间的信息传播过程更类似于随机游走,信息的传播途径可以是节点间的任一可达路径,在集聚系数高的网络中,节点的局部高聚簇性有利于信息的有效扩散,若只考虑信息按最优传播方式即最短路径传播,则会低估节点信息传播的能力,从而降低节点影响力的排序精度.综合考虑节点与三步内邻居间的有效可达路径以及信息传播率,提出了一种SP指标的改进算法,即ASP算法.在多个经典的实际网络和人工网络上利用SIR模型对传播过程进行仿真,结果表明ASP指标与度指标、核数指标、接近中心性指标、介数中心性指标以及SP指标相比,可以更精确地对节点传播影响力进行排序.