Model for Generating Scale-Free Artificial Social Networks Using Small-World Networks

The Internet of Things(IoT)has the potential to be applied to social networks due to innovative characteristics and sophisticated solutions that challenge traditional uses.Social network analysis(SNA)is a good example that has recently gained a lot of scientific attention.It has its roots in social and economic research,as well as the evaluation of network science,such as graph theory.Scientists in this area have subverted predefined theories,offering revolutionary ones regarding interconnected networks,and they have highlighted the mystery of six degrees of separation with confirmation of the small-world phenomenon.The motivation of this study is to understand and capture the clustering properties of large networks and social networks.We present a network growth model in this paper and build a scale-free artificial social network with controllable clustering coefficients.The random walk technique is paired with a triangle generating scheme in our proposed model.As a result,the clustering controlmechanism and preferential attachment(PA)have been realized.This research builds on the present random walk model.We took numerous measurements for validation,including degree behavior and the measure of clustering decay in terms of node degree,among other things.Finally,we conclude that our suggested random walk model is more efficient and accurate than previous state-of-the-art methods,and hence it could be a viable alternative for societal evolution.

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

We propose a modified susceptible-infected-refractory-susceptible （SIRS） model to investigate the global oscillations of the epidemic spreading in Watts-Strogatz （WS） small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on the spatico-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.

Nonlinear Dynamical Behavior in BS Evolution Model Based on Small-World Network Added with Nonlinear Preference

We introduce a modified small-world network adding new links with nonlinearly preferential connectioninstead of adding randomly,then we apply Bak-Sneppen(BS)evolution model on this network.We study severalimportant structural properties of our network such as the distribution of link-degree,the maximum link-degree,and thegth of the shortest path.We further argue several dynamical characteristics of the model such as the important criticalvalue f_c,the f_0 avalanche,and the mutating condition,and find that those characteristics show panticular behaviors.

Nonlinear Dynamical Behavior in BS Evolution Model Based on Small-World Network Added with Mechanism of Preferential Connection

In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen （BS） evolution model on this network. Several dynamical character of the model such as the evolution graph, fo avalanche, the critical exponent D and T, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.

Opinion Spreading with Mobility on Scale-Free Networks

A continuum opinion dynamic model is presented based on two rules. The first one considers the mobilities of the individuals, the second one supposes that the individuals update their opinions independently. The results of the model indicate that the bounded confidence εc, separating consensus and incoherent states, of a scale-free network is much smaller than the one of a lattice. If the system can reach the consensus state, the sum of all individuals＇ opinion change Oc（t） quickly decreases in an exponential form, while if it reaches the incoherent state finally, Oc（t） decreases slowly and has the punctuated equilibrium characteristic.

The classification and analysis of dynamic networks

In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M-G-P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M-G-P network is not only scale-free but also of a small-world feature in proper conditions.

A Novel Neighbor-Preferential Growth Scale-Free Network Model and its Properties

In this paper, we propose a novel neighbor-preferential growth (NPG) network model. Theoretical analysis and numerical simulations indicate the new model can reproduce not only a scale-free degree distribution and its power exponent is related to the edge-adding number m, but also a small-world effect which has large clustering coefficient and small average path length. Interestingly, the clustering coefficient of the model is close to that of globally coupled network, and the average path length is close to that of star coupled network. Meanwhile, the synchronizability of the NPG model is much stronger than that of BA scale-free network, even stronger than that of synchronization-optimal growth network.

Stability of weighted spectral distribution in a pseudo tree-like network model

The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution（i.e., a spectral graph feature） as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.

An application of small-world network on predicting the behavior of infectious disease on campus

Networks haven been widely used to understand the spread of infectious disease.This study examines the properties of small-world networks in modeling infectious disease on campus.Two different small-world models are developed and the behaviors of infectious disease in the models are observed through numerical simulations.The results show that the behavior pattern of infectious disease in a small-world network is different from those in a regular network or a random network.The spread of the infectious disease increases as the proportion of long-distance connections p increasing,which indicates that reducing the contact among people is an effective measure to control the spread of infectious disease.The probability of node position exchange in a network(p2)had no significant effect on the spreading speed,which suggests that reducing human mobility in closed environments does not help control infectious disease.However,the spreading speed is proportional to the number of shared nodes(s),which means reducing connections between different groups and dividing students into separate sections will help to control infectious disease.In the end,the simulating speed of the small-world network is tested and the quadratic relationship between simulation time and the number of nodes may limit the application of the SW network in areas with large populations.

Step-by-Step Random Walk Network with Power-Law Clique-Degree Distribution

We propose a simple mechanism for generating scale-free networks with degree exponent γ=3, where the new node is connected to the existing nodes by step-by-step random walk. It is found that the clique-degree distribution based on our model obeys a power-law form, which is in agreement with the recently empirical evidences. In addition, our model displays the small-world effect and the hierarchical structure.

复杂网络度分布特征研究

考察了复杂网络的不同模型,研究了在节点度总数不变条件下产生无标度现象的可能性。通过对OW S(择优W S)模型的提出和仿真,肯定了择优机制对形成网络节点度渐近分布特征的作用,并进一步指出,网络演化中进出择优机制的差异可能对其度分布特征产生重要影响。

基于小世界网络的知识网络结构演化模型研究

利用WS小世界网络模型构建知识网络的结构演化模型,通过度与度分布、平均最短路径长度及集聚系数等参数变化反映结构的时序变化,通过平均知识存量及标准差计算反映知识主体的行为变化,从而有助于明确知识网络结构演化微观动力机制及其结构演化过程细节。模型中知识网络主体的价值优化预期是网络结构演化动力,网络结构演化具体过程则涉及知识网络价值计算、知识节点耦合成本计算以及关系边权重计算三方面。

基于小世界网络模型的“梅特卡夫定律”反思

为了真正认清"网络中心战"的理论价值,对按照作为其理论支撑的"梅特卡夫定律"所规定的网络连接方式进行反思,定性分析了其带来的复杂性,并且应用小世界模型(WS)建立了复杂网络价值增益模型并进行了综合分析,发现实际网络不能够按照"梅特卡夫定律"的要求组网,指出"网络中心战"的理论缺陷,对我军信息化建设有一定的启示。

网络化防空作战C^2结构模型抗毁性

从网络动力学特征的角度,研究网络化防空作战C2结构模型抗毁性问题,针对以往的抗毁性测度指数不适用于C2网络抗毁性研究的现状,考虑C2网络信息融合的时延及战场感知覆盖率等因素,提出的抗毁性测度指标:最大连通片尺寸与网络规模比,最大连通片平均最短路径长度L,网络化效能系数。在指标的基础上对C2网络模型的抗毁性进行研究,并分析不同的空袭策略对防空作战C2网络抗毁性的影响。

小世界网络上流行病扩散控制策略

基于WS小世界网络和SIRS(Susceptible Infected Removed Susceptible)类流行病模型,通过数值模拟研究改变网络拓扑结构策略和改变网络拓扑结构与直接免疫相结合的策略对流行病扩散的控制。模拟结果显示,在第一种策略下,自我隔离的节点达到40%时疾病将在有限的时间内达到零感染态,而且随着自我隔离节点度被降低程度的升高疾病被控制的效果越好;在第二种策略下,疾病达到零感染态的速度比第一种策略下更快。两种策略都能够阻碍疾病的传染,控制疾病的蔓延,而且第二种策略的控制效果更佳。

基于给水管网建模技术对DMA分区的研究

应用InfoWorks WS软件建立某小区给水管网的水力模型.运用模型对该小区管网进行了分析,为该区作为分区装表计量技术的一个独立分区的设计方案提出了建议和意见.为其他区域合理性分区提供参考依据.

基于复杂性层级结构的神经网络组合研究

大脑大量的神经细胞数量和复杂的联系是处理信息的物质基础。由于包含神经元数量太少,现存各类人工神经网络难以胜任更加复杂的工作。复杂性理论的层级结构提供了以简单基本系统组建大规模系统的基本方法。神经解剖学关于大脑分区、分层、脑细胞垂直柱的概念,为构建基本子系统和实现子系统之间的连接提供了启示。在此基础上,以单个神经网络作为垂直柱单位的模拟,建立了组合神经网络的模型。基于这种可以包含大量神经元的模型,将有可能发展出适用于大规模信息处理的人工神经网络。

Using the contact network model and Metropolis-Hastings sampling to reconstruct the COVID-19 spread on the “Diamond Princess”

Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.

复杂网络的研究进展综述

网络由节点与连接节点之间的边组成。现实世界中存在大量的复杂系统可以用网络来描述。描述这些系统的网络既非完全规则又非完全随机,而是介于两者之间的。因此,介于规则网和随机网之间的复杂网能很好地刻画现实世界。本文介绍了复杂网络的发展史,研究现状及未来发展方向的展望。

复杂网络模型的分析

从平均路径长度、聚集系数、度分布的角度对复杂网络中的三种网络模型,即随机网络模型、小世界网络模型和无标度网络模型进行了分析,并对复杂网络模型的研究意义进行了说明.随着对复杂系统研究的深入,复杂网络在现实中的应用范围日益广泛,提供了一种新的方法去研究世界,同时也给带来新的机遇和挑战.