A local-world evolving hypernetwork model

Complex hypernetworks are ubiquitous in the real system. It is very important to investigate the evolution mechanisms. In this paper, we present a local-world evolving hypernetwork model by taking into account the hyperedge growth and local-world hyperedge preferential attachment mechanisms. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is γ = 2 + 1/m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient, as well as the average distance, and find that the hypernetwork model shares the scale-free and small-world properties, which shed some light for deeply understanding the evolution mechanism of the real systems.     

一种新型电力网络局域世界演化模型

现实世界中的许多系统都可以用复杂网络来描述,电力系统是人类创造的最为复杂的网络系统之一.当前经典的网络模型与实际电力网络存在较大差异.从电力网络本身的演化机理入手,提出并研究了一种可以模拟电力网络演化规律的新型局域世界网络演化模型.理论分析表明该模型的度分布具有幂尾特性,且幂律指数在3—∞之间可调.最后通过对中国北方电网和美国西部电网的仿真以及和无标度网络、随机网络的对比,验证了该模型可以很好地反映电力网络的演化规律,并且进一步证实了电力网络既不是无标度网络,也不是完全的随机网络. 关键词： 电力网络 演化模型 局域世界 幂律分布     

一种新型二分网络类局域世界演化模型

现实世界中复杂网络的演化存在很明显的局域选择现象,然而目前关于二分网络中的局域世界演化模型研究较少．因此,本文建立了一个基于二分网络的类局域世界演化模型．首先定义了网络节点度值的饱和度．在此基础上提出了一种新型二分网络局域世界演化模型．新节点加入系统不需要全局知识,而是通过节点在网络演化的不同时刻度值饱和度为选择条件构造新节点的局域世界,然后利用择优连接从局域世界中选择节点增加连边完成网络演化．此类模型中新节点的局域世界是通过节点饱和度的限制被动生成,因此又称为类局域世界模型．通过模拟分析发现在节点度值饱和度的限制下择优连接并没有产生具有幂率特性的度分布,而是生成了度分布相对均匀的二分网络,即节点度值分布区间较小．此外,本文还给出了该网络的混合系数计算结果,该结果显示网络同配性与网络参数的选择有关,这一结果与网络邻点平均度的模拟结果一致．     

A local-world node deleting evolving network model

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting.     

An evolving network model with modular growth

In this paper, we propose an evolving network model growing fast in units of module, according to the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing the ratio of the number of inner-module edges and the number of inter-module edges. In view of the mean-field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module.     

基于超图结构的科研合作网络演化模型

基于科研论文作者的合作方式, 用超图理论构建了一个科研合作超网络演化模型. 利用平均场理论分析了作者发表论文的演化规律, 发现作者的超度 (即发表论文数) 分布符合幂律分布. 进一步理论分析得到分布的幂指数γ与合作领域作者增长速度相关. γ越大, 新作者增长速度越快, 且存在关系: γ=1+L/M (L/M为作者增长率). 并通过对《物理学报》与《中国科学》2003–2012年期间作者发表论文进行了数据分析, 实证结果与理论分析及模拟结果能很好地符合. 本文对科研合作网络的理论和实证研究有一定的借鉴意义. 关键词： 复杂网络 超图 科研合作网络 演化模型     

基于Sierpinski分形垫的确定性复杂网络演化模型研究

近年来,人们发现大量真实网络都表现出小世界和无尺度的特性,由此复杂网络演化模型成为学术界研究的热点问题.本文基于Sierpinski分形垫,通过迭代的方式构造了两个确定性增长的复杂网络模型,即小世界网络模型(S-DSWN)和无尺度网络模型(S-DSFN);其次,给出了确定性网络模型的迭代生成算法,解析计算了其主要拓扑特性,结果表明两个网络模型在度分布、集聚系数和网络直径等结构特性方面与许多现实网络相符合;最后,提出了一个确定性的统一模型(S-DUM),将S-DSWN与S-DSFN纳入到一个框架之下,为复杂网络的相关研究提供理论基础.特别地,发现这些网络模型都是极大平面图.     

The physical position neighbourhood evolving network model

Many social, technological, biological and economical systems are properly described by evolved network models. In this paper, a new evolving network model with the concept of physical position neighbourhood connectivity is proposed and studied. This concept exists in many real complex networks such as communication networks. The simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of the graph Laplacian, clustering coefficients, average distances and degree distributions for different evolving parameters of this model are presented. The dynamical behaviour of each node on the consensus problem is also studied. It is found that the degree distribution of this new model represents a transition between power-law and exponential scaling, while the Barábasi-Albert scale-free model is only one of its special (limiting) cases. It is also found that the time to reach a consensus becomes shorter sharply with increasing of neighbourhood scale of the nodes.     

Epidemic propagation on adaptive coevolutionary networks with preferential local-world reconnecting strategy

In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR- SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.     

权重分布对加权局域世界网络动力学同步的影响

加权网络可以更细致地刻画复杂系统中两节点之间的相互作用, 所以加权网络也比无权网络更接近真实的复杂系统. 改变权重分布来调节和改善复杂网络的性质也成为一种新的研究方法. 基于现有无权网络同步的概念, 应用特征值比R来衡量加权局域世界网络的同步能力, 发现权重分布对加权局域世界网络的同步能力有很重要的影响, 权重分布越均匀, 网络的同步能力就越大. 关键词： 权重分布 局域世界 加权网络 同步     

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.     

一种基于随机行走和策略连接的网络演化模型

本文提出了一个基于随机行走和策略选择的复杂网络局域演化模型RAPA. 新节点加入系统不需要全局知识,而是通过随机行走构造局域世界;然后依据概率采用随机连接,"扶贫"连接或"亲富"连接策略,从局域世界中选择节点增加连接边;最终自组织演化具有幂律特点的复杂网络. 初步的解析计算和仿真实验都表明,RAPA模型不仅重现了具有小世界特性、整体上的无标度特性,还可以演化出小变量饱和以及指数截断等现象,同时也具有明显的聚类特性,并能够构造出同配或异配等不同混合模式的网络. 关键词： 复杂网络 模型 随机行走 策略连接     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.     

基于Web 2.0的边与节点同时增长网络模型

模拟了Web2.0网络的发展过程并研究其拓扑结构,分析某门户网站实际博客数据的度分布、节点度时间变化,发现与先前的无标度网络模型有所差别.根据真实网络的生长特点,提出了边与节点同时增长的网络模型,包括随机连接及近邻互联的网络构造规则.仿真研究表明,模拟的网络更接近实际,在没有优先连接过程时,模型能得到幂率的度分布;并且网络有更大的聚类系数以及正的度相关性。     

一类权重网络的加速演化模型

采用动态形成权重网络的方法，研究了在演化过程中新增边具有加速连接情况下权重网络的拓扑特性和强度分布，给出了节点强度与度的解析表达式.分析表明，加速演化的权重模型具有明显的无标度特性.再者，只要权重网络的边权重服从某一概率分布，则在演化过程中强度择优连接与度择优连接对于网络的度分布没有影响，且与具体的概率分布无关.     

复杂网络局部结构的涌现:共同邻居驱动网络演化

在对真实网络的小世界和无标度特性进行了大量深入考量之后,最近的研究热点开始转移到更加细致的局部结构.实证数据显示,大量真实网络具有幂律的低阶集团度分布.这一普适的规律,无法由富者愈富以及熟人推荐的网络生长机理再现.本文提出一种由共同邻居驱动的网络演化模型,该模型能够重现实证研究所观察到的幂律集团度分布,暗示共同邻居驱动是复杂网络局部结构涌现形成的内在机理. 关键词： 复杂网络 演化模型 集团度分布 共同邻居     

基于平均场理论的微博传播网络模型

微博是在通过用户关注机制建立的用户网络上分享实时信息的社交平台,而微博消息主要通过用户的转发行为使消息在用户网络上传播.掌握微博消息的传播机制,对研究微博上舆论谣言的传播、产品推广等具有指导作用.本文通过对微博传播网络的结构分析来探索微博传播过程,利用新浪微博数据,建立微博传播网络,分析该网络的生成机制,使用平均场论的方法,推导微博传播网络的度分布模型.实验结果表明:微博传播网络的度分布是时间相依的,在特定时间下网络的度分布服从幂律分布.     

A general evolving model for growing bipartite networks

In this Letter, we propose and study an inner evolving bipartite network model. Significantly, we prove that the degree distribution of two different kinds of nodes both obey power-law form with adjustable exponents. Furthermore, the joint degree distribution of any two nodes for bipartite networks model is calculated analytically by the mean-field method. The result displays that such bipartite networks are nearly uncorrelated networks, which is different from one-mode networks. Numerical simulations and empirical results are given to verify the theoretical results.