群体行为的异质节点复杂网络传播

当遭遇突发的公共社会安全事件时,具有负面影响的应激行为可能迅速在社会范围内传播扩散,形成群体行为.虽然一些复杂网络的传染模型能够对此进行刻画,但更为符合实际的是行为群体根据一些特性可能划分为不同的亚群体,为此将建立异质节点SIS复杂网络模型.此后,依据亚群体的有效传播率与度分布无关、正相关和负相关三种情形,分别研究了群体行为在异质节点的小世界网络传播特性,及异质节点的无标度网络传播特性.无论是异质节点的小世界网络模型还是异质节点的无标度网络模型,平均场动力学分析和计算机模拟结果显示,当亚群体的传播率与度分布呈正相关时,群体行为的传播会出现放大相应;反之,当亚群体的传播率与度分布成负相关时,群体行为的传播会出现抑制效应.但以上的两种效应在离散性更强的无标度网络上更为明显.     

BA模型的数学基础——纪念李国平院士吴新谋教授诞辰100周年

该文基于马氏链的概念和技巧, 给出了BA无标度网络模型稳态度分布存在性的严格证明, 并且从数学上重新推导了度分布的精确解析表达式. 此处所用的方法具有一定的普适性, 适用于更一般的无标度型复杂网络模型.     

BA模型的数学基础

该文基于马氏链的概念和技巧,给出了BA无标度网络模型稳态度分布存在性的严格证明,并且从数学上重新推导了度分布的精确解析表达式.此处所用的方法具有一定的普适性,适用于更一般的无标度型复杂网络模型.     

基于度与路径优先连接的集聚型供应链网络演化模型

集聚型供应链供应链网络具有无标度性、高集聚性等特征.以往研究忽视了供应链网络的高集聚性,使得供应链网络模型不能够准确刻画实际的集聚型供应链网络.本文在具体分析集聚型供应链网络动态演化特征的基础上,提出了基于度与路径优先连接的集聚型供应链网络演化模型,弥补了优先连接仅依赖于节点度值的不足.最后,对集聚型供应链网络的度分布、集聚系数和平均最短路径参数进行了数值模拟,模拟结果表明,该模型不仅能够反映集聚型供应链网络的无标度性,而且能够真实刻画其高集聚性特征.     

一类点边同时变化的增长网络的度分布

本文研究一个节点和连边能同时发生变化的网络模型,把模型中的节点度的演化过程看成一族马氏链。从模型的演化机制中得到该马氏链的状态转移概率,用马氏链的方法证明了该模型的稳态度分布是存在的,并得到了度分布的精确表达式。从而说明了该网络是标度指数为3的无标度网络。     

节点的时间异质性对信息传播的影响

复杂系统中节点活跃时间的异质性对信息传播具有显著性的影响,而现有的研究涉及较少.文章引入传播树模型针对复杂网络中节点活跃时间的异质性对信息传播的影响进行研究,基于SI模型的传染病机制,运用生成函数方法严格证明了当节点的活跃时间服从伽马型概率分布时,节点的信息传播影响力的变化具有多态性,即传播时间t在小于时间标度τ~0时,感染节点数服从指数分布,而在大于时间标度τ~0时,感染节点数服从多项式分布。     

随机增长网络的度分布

增长和择优机制是无标度网络中的两种重要的演化机制,在分析BA模型的基础上,提出了一种新的节点增长方式,即考虑了新增节点的连边数是随机变量的情况,从而建立了随机增长网络模型,并利用随机过程理论得到了在这种增长方式下网络的度分布,结果表明这个网络是无标度网络。     

随机连接广义合作网络模型

本文提出了一个项目参与者数T是随机变量的广义合作网络模型,新节点与随机选择的节点合作,通过节点度演化所满足的马尔可夫性,利用马．尔可夫链的方法和技巧得到了度分布的精确解析表达式．并说,明了此广义合作网络不是无标度网络．     

无标度网络演化过程中的结构熵

熵是度量复杂系统无序性的重要物理量,而且现实中的大多数网络都呈现出无标度网络的特性.在网络的节点熵和结构熵概念的基础上,给出了BA模型的网络结构熵演化的解析结论和数值模拟.从解析结论和数值模拟可以得到,网络结构熵随网络大小以对数的速度增长;但在同样规模下,无标度网络的结构熵小于随机网络的结构熵.     

多社团加权复杂网络建模及其级联抗毁性研究

为了研究社团结构和权重因素对网络级联抗毁性的影响,引入节点和边的消亡机制,建立了一类具有社团结构的加权网络模型.采用本方法生成网络的度、强度和边权分布都呈现无标度特性,比现有BBV (Barrat-Barthelemy-Vespignani)模型具有更好的社团结构特性,且幂律指数、模块度参数可调.在此基础上研究了网络的级联抗毁性,采用节点及其邻居节点强度的函数定义网络负荷,故障节点负荷采用"局部定义,局部分配"的策略.仿真分析了边权演化参数、模块度函数、攻击策略和演化时间对网络级联抗毁性的影响.结论表明,网络的抗毁性与边权演化参数、网络演化时间成反比,与模块度的关系不是单调的而是存在一个阈值.优先攻击度最大节点的策略对网络抗毁性破坏最大,且在多节点遭受攻击时,网络的故障规模会发生突变.文章的研究结论对故障的预防与控制以及网络的建设具有一定的参考价值.     

Poisson增长竞争网络与适应度模型

提出吸引度依赖于时间的竞争网络模型.利用Poisson过程获得这个模型稳态平均度分布的解析表达式.理论分析表明,这类网络幂律指数与渐近吸引系数和新节点边数m有关,且在区间(1+1/m,m+1)内.作为竞争网络模型的应用,获得了适应度模型的度分布估计.结果表明适应度模型是竞争网络模型的特例,反之则不然.     

基于二项分布随机增长的无标度网络

提出—个具有随机增长的无标度网络模型．该模型的演化规则仍然是BA模型的增长和择优连接,但是每一时间间隔添加到网络中的边数是—个具有二项分布的随机变量．通过率方程方法,本文证明了该网络的度分布具有幂律尾部,该模型生成了—个无标度网络．     

基于复杂网络的中国股市房地产板块股票强相关性研究

为分析中国股市房地产板块股票的强相关特性,以101只股票为结点,以近17年股票对数回报的相关系数为加权边,建立复杂网络模型,通过对网络拓扑参数计算,发现该网络为无尺度网络,结点度分布P(s)~s-|s|δ,在不同相关系数阈值下,δ值介于0.8~1.6之间.网络平均集聚系数为0.53.文章也对网络中心性进行测量和子群划分,发现代码为000592和601588的结点在网络中具有很高的中介性,网络中大部分结点都受其影响较大.     

The different cooperative behaviors on a kind of scale-free networks with identical degree sequence

The power-law degree distribution of scale-free networks plays an important role in the bloom of cooperation in the evolutionary games performed on them. In this paper we apply prisoner’s dilemma and public goods game on a family of scale-free networks with the same degree sequence, and show that power-law behavior alone does not determine the cooperative behavior in scale-free networks. Instead, we present that the direct connections among large-degree nodes have a crucial influence on the evolution of cooperation in the scale-free network family.     

Scientific collaboration network of Turkey

Networking via co-authorship is an important area of research and used in many fields such as ranking of the universities/departments. Studying on the data supplied by the Web of Science, we constructed a structural database that defines the scientific collaboration network of the authors from Turkey, based on the publications between 1980 and 2010. To uncover the evolution and structure of this complex network by scientific means, we executed some empirical measurements. The Turkish scientific collaboration network is in an accelerating phase in growth, highly governed by the national policies aiming to develop a competitive higher education system in Turkey. As our results suggest the authors tend to make more number of collaborations in their studies over the years. The results also showed that, node separation of the network slightly converges about 4, consistent with the small world phenomenon. Together with this key indicator, the high clustering coefficient, (which is about 0.75) reveals that our network is strongly interconnected. Another quantity of major interest about such networks is, “the degree distribution”. It has a power-law tail that defines the network as scale-free. Along with the final values, the time evolutions of the above-mentioned parameters are presented in detail with this work. In a good agreement with the recent studies, our network yields some significant differences especially in growing rate, clustering properties and node separation. In contrast with the recent studies, we also showed that preferring to attach popular nodes result with being a more popular node in the future.     

产学研合作创新网络规模、连接机制与创新绩效的关系研究——基于多主体仿真和动态系统论视角

为揭示产学研合作创新网络规模与连接机制对创新绩效的影响机理,运用Agent建模理论和Netlogo仿真平台构建产学研合作创新网络的仿真模型,对不同特性(小世界、无标度)偏好下的产学研合作创新网络进行仿真实验,并运用动态系统理论解释仿真的涌现现象。研究发现:①网络平均节点度(度数中心势)与网络平均创新绩效(节点加权平均收益的对数)之间存在鞍结分叉和跨临界分叉的组合现象;②网络平均距离(关系强度)与网络平均绩效之间呈指数增长分布轨道;③连接机制与网络平均绩效呈对数增长分布轨道;④实力择优连接机制提升网络平均节点度正向作用的效率较低;⑤随机组合择优连接机制更有利于提升小世界偏好网络平均距离的正向作用;⑥度择优连接机制更有利于提升无标度偏好网络平均创新绩效。     

Naming Game with Multiple Hearers

A new model called Naming Game with Multiple Hearers (NGMH) is proposed in this paper. A naming game over a population of individuals aims to reach consensus on the name of an object through pair-wise local interactions among all the individuals. The proposed NGMH model describes the learning process of a new word, in a population with one speaker and multiple hearers, at each interaction towards convergence. The characteristics of NGMH are examined on three types of network topologies, namely ER random-graph network, WS small-world network, and BA scale-free network. Comparative analysis on the convergence time is performed, revealing that the topology with a larger average (node) degree can reach consensus faster than the others over the same population. It is found that, for a homogeneous network, the average degree is the limiting value of the number of hearers, which reduces the individual ability of learning new words, consequently decreasing the convergence time; for a scale-free network, this limiting value is the deviation of the average degree. It is also found that a network with a larger clustering coefficient takes longer time to converge; especially a small-word network with smallest rewiring possibility takes longest time to reach convergence. As more new nodes are being added to scale-free networks with different degree distributions, their convergence time appears to be robust against the network-size variation. Most new findings reported in this paper are different from that of the single-speaker/single-hearer naming games documented in the literature.     

EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK

In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.