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     

Different Epidemic Models on Complex Networks

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.     

基于感知流量算法的复杂网络拥塞问题研究

研究了在具有感知流量的路由策略下,复杂网络的拓扑结构对网络中传输流量的影响.为了描述数据包传输过程的有效性,通过引入一个状态参数,利用由稳态到拥塞的指标流量相变值来刻画网络的吞吐量.基于每个节点的数据包处理能力与该节点的度或介数成比例提出两种模型并进行仿真.仿真结果表明,平均度相同的情况下,模型Ⅰ中,WS小世界网络比ER随机网络和BA无标度网络更容易产生拥塞;模型Ⅱ中,所有网络容量都得到较大的提高,尤其是WS小世界网络.但当网络的基本连接参数改变时,哪种模型更利于网络的流量传输,还要依据网络本身的结构特性关键词：复杂网络无标度网络感知流量拥塞     

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     

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     

具有非均匀传输和抗攻击差异的网络病毒传播模型

针对实际网络中节点存在抗攻击差异以及边的非均匀传输等情况,基于平均场理论,提出具有抗攻击差异和非均匀传输特性的网络病毒传播平均场SIR模型.该模型中,通过引入脆弱性函数和传输函数,分别描述节点的抗攻击差异以及边的非均匀传输能力.通过对所提模型的分析,得到传播阈值的理论结果.理论分析和仿真表明,节点的抗攻击差异以及边的非均匀传输,都可导致出现正的传播阈值,使得病毒传播风险有效降低.     

基于节点度信息的自愿免疫模型研究

疾病的广泛传播给人类带来了巨大的损失, 因此抑制疾病的传播非常重要. 本文考虑了个体接种疫苗意愿的差异性, 并结合博弈理论建立了一个基于节点度信息的自愿免疫模型. 理论解析结果证明当感染率超过某个阈值时, 该模型与忽略个体接种意愿差异性的经典模型(Zhang et al 2010 New J. Phys. 12 023015) 传播效果(感染节点数)一样. 继而考虑疫苗永久有效和有效期有限两种情况, 在Barabási-Albert网络中利用SIS传播模型对疾病的传播进程进行了数值模拟, 发现数值模拟结果与理论解析结果非常符合. 实验证明, 当感染耗费和接种疫苗耗费相同时, 该模型比忽略个体接种意愿差异性的经典模型能够更好的抑制疾病的传播, 且感染人数下降比例超过65%, 更重要的是,疫苗有效期越长本文的模型 (与忽略个体接种意愿差异性的经典模型相比)抑制疾病传播效果越好.关键词：疾病传播自愿免疫接种疫苗倾向节点度     

Epidemic spreading in complex networks

The study of epidemic spreading in complex networks is currently a hot topic and a large body of results have been achieved. In this paper, we briefly review our contributions to this field, which includes the underlying mechanism of rumor propagation, the epidemic spreading in community networks, the influence of varying topology, and the influence of mobility of agents. Also, some future directions are pointed out.      

一种基于点和边差异性的网络结构熵

熵是反映网络异构性的重要指标. 由于只是关注网络结构中\"点\"或\"边\"的单一作用,基于度分布和度相对值的两种传统熵在刻画网络结构特征时均存在缺陷. 文章综合考虑\"点\"和\"边\"差异性,定义一种新的网络结构熵,并对规则网络、随机网络和无标度网络等结构熵进行理论分析和仿真实验. 结果表明,这种新网络结构熵可以更有效地反映网络的结构特征,尤其是对于稀疏网络及星型网络的结构差异解释更为合理.关键词：均匀网络无标度网络熵     

Weighted scale-free networks with variable power-law exponents

We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.     

一种可大范围调节聚类系数的加权无标度网络模型

在Barrat, Barthélemy 和 Vespignani (BBV)加权无标度网络模型的基础上,提出了一种可大范围调节聚类系数的加权无标度网络模型——广义BBV模型(GBBV模型).理论分析和仿真实验表明,GBBV模型保留了BBV模型的许多特征,节点度、节点权重和边权值等都服从幂律分布.但是,GBBV模型克服了BBV模型只能小范围调节聚类系数的缺陷,从而可以用于具有大聚类系数网络的建模.关键词：无标度网络加权网络聚类系数     

无标度网络上队列资源分配研究

研究了节点队列资源有限的条件下,无标度网络上的信息流动力学过程,发现了网络由自由流通到拥塞的相变现象,提出了一种基于节点度的队列资源分配模型.模型的核心是使节点i的队列长度与kβi成正比(ki为节点i的度,β为分配参数).仿真结果表明,在网络使用最短路径算法进行信息包传送的条件下,β近似等于1.25时队列资源分配最合理,网络容量最大,且该最佳值与队列总资源多少以及网络的规模无关.     

Co-evolution of the brand effect and competitiveness in evolving networks

The principle that ‘the brand effect is attractive’ underlies the preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly introduce a general framework that allows us to investigate the competitive aspect of real networks, instead of simply preferring popular nodes. Our model accurately describes the evolution of social and technological networks. The phenomenon that more competitive nodes become richer can help us to understand the evolution of many competitive systems in nature and society. In general,the paper provides an explicit analytical expression of degree distributions of the network. In particular, the model yields a nontrivial time evolution of nodes’ properties and the scale-free behavior with exponents depending on the microscopic parameters characterizing the competition rules. Secondly, through theoretical analyses and numerical simulations, we reveal that our model has not only the universality for the homogeneous weighted network, but also the character for the heterogeneous weighted network. Thirdly, we also develop a model based on the profit-driven mechanism. It can better describe the observed phenomenon in enterprise cooperation networks. We show that the standard preferential attachment,the growing random graph, the initial attractiveness model, the fitness model, and weighted networks can all be seen as degenerate cases of our model.     

扩展HK网络结构与同步能力的研究

研究两种高聚类系数无标度网络演化机理对网络同步能力的影响．首先,以Holme和Kim（HK）模型为基础,提出了度分布和聚类系数均可调的扩展HK模型（EHK模型）．扩展HK模型将HK模型中的三角结构扩展到了旧节点之间,解决了HK模型边的演化只存在新旧节点之间以及每个时间步加入网络节点的边数固定的不足．其次,研究了三角结构演化机理对网络同步能力的影响．最后,仿真研究发现三角结构的演化机理降低了两类无权网络的同步能力．     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.