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     

蛋白质相互作用网络特征的理论再现

无标度性、小世界性、功能模块结构及度负关联性是大量生物网络共同的特征. 为了理解生物网络无标度性、小世界性和度负关联性的形成机制, 研究者已经提出了各种各样基于复制和变异的网络增长模型. 在本文中,我们从生物学的角度通过引入偏爱小复制原则及变异和非均匀的异源二聚作用构建了一个简单的蛋白质相互作用网络演化模型.数值模拟结果表明,该演化模型几乎可以再现现在实测结果所公认的蛋白质相互作用网络的性质：无标度性、小世界性、度负关联性和功能模块结构. 我们的演化模型对理解蛋白质相互作用网络演化过程中的可能机制提供了一定的帮助. 关键词： 蛋白质相互作用网络 偏爱小 非均匀的异源二聚作用 功能模块结构     

超网络中标度律的涌现

本文构建超网络和复杂网络中统一演化模型,研究超网络无标度特性演化机理和拓扑性质.利用Poisson过程理论和连续化方法对模型进行分析,获得网络稳态平均超度分布的解析表达式.仿真实验和理论分析相符合.结果表明:随着网络规模的增大,这个动态演化网络的超度分布遵循无标度的特性.它不仅将每次增加一个新节点与若干个老节点围成一条超边的超网络模型和每次增加若干个新节点与一个老节点围成一条超边的超网络模型统一在一个模型中,而且将复杂网络中著名的无标度模型也作为我们模型的特例.     

一种强容侵能力的无线传感器网络无标度拓扑模型研究

针对无线传感器网络无标度拓扑容侵能力差的问题,本文借助节点批量到达的Poisson网络模型,提出了一种具有容侵优化特性的无标度拓扑模型,并在构建拓扑时引入剩余能量调节因子和节点度调节因子,得到了一种幂率指数可以在(1,+∞)调节的无标度拓扑结构,并通过网络结构熵优化幂率指数,得出了具有强容侵特性的幂律指数值.实验结果表明:新的拓扑保持了无标度网络的强容错性,增强了无标度网络的容侵性,并具有较好的节能优势.     

增长及非增长无标度网络的成因解析

分析两类无标度网络的形成原因,提出一个无标度网络演化模型并进行一系列数值实验.基于分析和实验得到推论:只要保持足够低的网络密度,通过基于度的偏好连接就可形成长期稳定的无标度网络.规模增长和点边增删既是客观存在,又起到了控制网络密度的作用,足够低的网络密度和基于度的偏好连接是所有无标度网络共同的必要条件.推论可同时解释增长和非增长无标度网络的形成原因.研究结果有助于理解各种真实无标度网络和建立相应的模型.     

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     

基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.     

一种基于最大流的网络结构熵

熵是可用来反映网络结构异质性的指标.针对传统熵指标不能很好反映网络全局异构性的不足,本文引入网络流的概念,综合考虑径向测度和中间测度,提出一种新的网络结构熵.特殊网络(如公用数据集Dolphins网络)的分析结果表明,本文提出的熵指标在一定程度上克服了其他网络熵指标的不足,更能够反映网络的真实拓扑结构;对随机网络、最近邻耦合网络、星型网络、无标度网络、Benchmark网络和小世界网络等典型网络的理论分析和仿真实验,进一步证明本文提出的熵指标在刻画一般复杂网络结构特征上的有效性和适用性.     

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     

能量异构的无线传感器网络加权无标度拓扑研究

针对无线传感器网络节点能耗不均和如何高效获得节点和边的负载问题,提出一种局域范围内能量异构的加权无标度拓扑演化模型.通过对节点能量与负载、能耗的关系建模,建立节点能量与点权和边权的联系,进而结合点权和加权模型给出网络的演化方式,推出点权、度和边权的幂率分布规律,最终根据网络获得的点权和边权来分析负载和能耗.仿真结果表明,提出的模型不仅能够准确计算点边的负载,而且缓解了无标度网络的节点能耗不均衡问题.     

基于信息熵的社交网络观点演化模型

随着网络服务的发展,社交网络逐渐成为信息传播的新媒介.因此,研究网络舆情演化具有重要意义和实用价值.为了更好地研究网络舆论,在信息熵的基础上,提出了一个社交网络观点演化模型.此模型存在以下两个特点:一是可以反映个体面对正负两种观点趋向做出抉择时的心理过程;二是可以反映个体形成新观点时主观因素和客观因素的影响.在仿真实验中,讨论了舆论环境对个体观点演化的影响,初始观点和自信度对观点演化的影响,以及意见领袖对群体观点演化的影响.实验结果表明,该模型可以反映真实社交网络中个体的心理学特征,比如个体的观点形成会受到舆论环境的影响,自信的个体不愿意接受他人的观点,当意见领袖存在时群体的观点会受到影响等.     

Outward-inward information flux in an opinion formation model on different topologies

A simple model of opinion formation dynamics in which binary-state agents make up their opinions due to the influence of agents in a local neighborhood is studied using different network topologies. Each agent uses two different strategies, the Sznajd rule with a probability q and the Galam majority rule (without inertia) otherwise; being q a parameter of the system. Initially, the binary-state agents may have opinions (at random) against or in favor about a certain topic. The time evolution of the system is studied using different network topologies, starting from different initial opinion densities. A transition from consensus in one opinion to the other is found at the same percentage of initial distribution no matter which type of network is used or which opinion formation rule is used.     

Dynamics of opinion formation in hierarchical social networks: Network structure and initial bias

The dynamics of opinion formation based on a majority rule model is studied in a network with the social hierarchical structure as one of its limits. The exit probability is found to change sensitively with the number of nodes in the system, but not with the parameter of homophyly characterizing the network structure. The consensus time is found to be a result of non-trivial interplay between the network structure characterized by the parameter of homophyly and the initial bias in opinion. For unbiased initial opinion, a common consensus is easier to be reached in a random network than a highly structured hierarchical network and it follows the behavior of the length of shortest paths. For biased initial opinion, a common consensus is easier to be reached in a hierarchical network, as the local majority opinion of the groups may take on the biased opinions and hence be the same.     

Social bots and mass media manipulated public opinion through dual opinion climate

Opinion dynamics models based on the multi-agent method commonly assume that interactions between individuals in a social network result in changes in their opinions.However,formation of public opinion in a social network is a macroscopic statistical result of opinions of all expressive individuals(corresponding to silent individuals).Therefore,public opinion can be manipulated not only by changing individuals'opinions,but also by changing their states of expression(or silence)which can be interpreted as the phenomenon"spiral of silence"in social psychology.Based on this theory,we establish a"dual opinion climate"model,involving social bots and mass media through a multi-agent method,to describe mechanism for manipulation of public opinion in social networks.We find that both social bots(as local variables)and mass media(as a global variable)can interfere with the formation of public opinion,cause a significant superposition effect when they act in the same direction,and inhibit each other when they act in opposite directions.     

Non-consensus Opinion Models on Complex Networks

Social dynamic opinion models have been widely studied to understand how interactions among individuals cause opinions to evolve. Most opinion models that utilize spin interaction models usually produce a consensus steady state in which only one opinion exists. Because in reality different opinions usually coexist, we focus on non-consensus opinion models in which above a certain threshold two opinions coexist in a stable relationship. We revisit and extend the non-consensus opinion (NCO) model introduced by Shao et al. (Phys. Rev. Lett. 103:01870, 2009). The NCO model in random networks displays a second order phase transition that belongs to regular mean field percolation and is characterized by the appearance (above a certain threshold) of a large spanning cluster of the minority opinion. We generalize the NCO model by adding a weight factor W to each individual’s original opinion when determining their future opinion (NCOW model). We find that as W increases the minority opinion holders tend to form stable clusters with a smaller initial minority fraction than in the NCO model. We also revisit another non-consensus opinion model based on the NCO model, the inflexible contrarian opinion (ICO) model (Li et al. in Phys. Rev. E 84:066101, 2011), which introduces inflexible contrarians to model the competition between two opinions in a steady state. Inflexible contrarians are individuals that never change their original opinion but may influence the opinions of others. To place the inflexible contrarians in the ICO model we use two different strategies, random placement and one in which high-degree nodes are targeted. The inflexible contrarians effectively decrease the size of the largest rival-opinion cluster in both strategies, but the effect is more pronounced under the targeted method. All of the above models have previously been explored in terms of a single network, but human communities are usually interconnected, not isolated. Because opinions propagate not only within single networks but also between networks, and because the rules of opinion formation within a network may differ from those between networks, we study here the opinion dynamics in coupled networks. Each network represents a social group or community and the interdependent links joining individuals from different networks may be social ties that are unusually strong, e.g., married couples. We apply the non-consensus opinion (NCO) rule on each individual network and the global majority rule on interdependent pairs such that two interdependent agents with different opinions will, due to the influence of mass media, follow the majority opinion of the entire population. The opinion interactions within each network and the interdependent links across networks interlace periodically until a steady state is reached. We find that the interdependent links effectively force the system from a second order phase transition, which is characteristic of the NCO model on a single network, to a hybrid phase transition, i.e., a mix of second-order and abrupt jump-like transitions that ultimately becomes, as we increase the percentage of interdependent agents, a pure abrupt transition. We conclude that for the NCO model on coupled networks, interactions through interdependent links could push the non-consensus opinion model to a consensus opinion model, which mimics the reality that increased mass communication causes people to hold opinions that are increasingly similar. We also find that the effect of interdependent links is more pronounced in interdependent scale free networks than in interdependent Erd?s Rényi networks.     

An evolutionary game theory model of binary opinion formation

A basic characteristic of most opinion models is that people tend to agree or compromise in the opinion interaction, which could be hopefully described by cooperative games in the evolutionary game theory framework. This paper presents game theory methods to model the formation of binary opinions: cooperative games are proposed to model the interaction rules of general people who tend to find an agreement; minority games are proposed to model the behaviors of contrarians; opinion preference is considered by varying the payoff values. The Majority Voter model could be restored from the proposed games. The game theory models show evolutionary results similar to traditional opinion models. Specially, the evolution of opinions with consideration of contrarians is in accordance with the Galam model. Furthermore, influences of evolving rule, network topology and initial distribution of opinions are studied through numerical simulations. Discussions about methods to promote or hinder the consensus state at the best equilibrium point are given.     

Symmetry breaking in the opinion dynamics of a multi-group project organization

A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group’s opinion evolution is driven by two types of forces:(i) the group’s cohesive force which tends to restore the opinion back towards the initial status because of its company culture;and(ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness.Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes,i.e.,a deadlock regime,a convergence regime,and a bifurcation regime in opinion dynamics.The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to.In the case of a three-group project with a symmetric social network,both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord,instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay’s result(Physica A 378(2007) p.125 Fig.5),project organization(PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations,which urges that apart from divergence in participants’ interests,nonlinear interaction can also make conflict inevitable in the PO.The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO.It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.     

基于混沌理论和改进径向基函数神经网络的网络舆情预测方法

网络舆情发展趋势具有混沌系统的特征, 提出一种基于EMPSO-RBF神经网络的方法对网络舆情的发展趋势进行预测. 首先根据Lyapunov指数证明网络舆情具备混沌的特征, 然后对网络舆情时间序列数据进行相空间重构, 最后采用EMPSO-RBF方法进行预测, 并和其他模型进行对比试验, 实验结果表明EMPSO-RBF方法具有较高精确度.     

基于新曝光冲突性消息的网络舆论逆转研究

对网络舆论逆转过程进行研究具有十分重要的意义,它有助于管理者有效引导舆论朝良性方向发展.目前,网络舆论逆转研究主要集中于动力学模型构建与仿真实验分析,其研究结果具有一定的理论价值.然而,这是否适用于真实社交网络环境,还尚未经过测试.为了对舆论逆转过程进行研究,构建了符合实际的模型,并对网络舆论逆转典型事例进行了深入分析.通过观察统计,发现网络舆论逆转具有自身的规律:新曝光冲突性消息是导致舆论发生逆转的根本原因;消息的传播影响着群体的发声与沉默;消息的属性包括传播率、可信度、观点倾向、起始传播时间和消息源中心度决定着舆论逆转的幅度.依据这一规律,设置了消息属性参数,并将消息传播与观点演化过程相结合,构建了网络舆论逆转模型.模型的仿真实验结果表明,新冲突性消息的传播率、可信度和消息源中心度正向影响着舆论逆转幅度,其中可信度较传播率影响更大.新的冲突性消息曝光的时间越早,舆论逆转的速率越快,幅度越大.该模型与实际相符,可为理解和解释网络舆论逆转过程、引导网络舆论提供理论依据.     

Towards understanding the behavior of physical systems using information theory

One of the goals of complex network analysis is to identify the most influential nodes, i.e., the nodes that dictate the dynamics of other nodes. In the case of autonomous systems or transportation networks, highly connected hubs play a preeminent role in diffusing the flow of information and viruses; in contrast, in language evolution most linguistic norms come from the peripheral nodes who have only few contacts. Clearly a topological analysis of the interactions alone is not sufficient to identify the nodes that drive the state of the network. Here we show how information theory can be used to quantify how the dynamics of individual nodes propagate through a system. We interpret the state of a node as a storage of information about the state of other nodes, which is quantified in terms of Shannon information. This information is transferred through interactions and lost due to noise, and we calculate how far it can travel through a network. We apply this concept to a model of opinion formation in a complex social network to calculate the impact of each node by measuring how long its opinion is remembered by the network. Counter-intuitively we find that the dynamics of opinions are not determined by the hubs or peripheral nodes, but rather by nodes with an intermediate connectivity.