Weighted Evolving Networks with Self-organized Communities

In order to describe the self-organization of communities in the evolution of weighted networks, we propose a new evolving model for weighted community-structured networks with the preferential mechanisms functioned in different levels according to community sizes and node strengths, respectively. Theoretical analyses and numerical simulations show that our model captures power-law distributions of community sizes, node strengths, and link weights, with tunable exponents of ν≥1, γ>2, and α>2, respectively, sharing large clustering coefficients and scaling clustering spectra, and covering the range from disassortative networks to assortative networks. Finally, we apply our new model to the scientific co-authorship networks with both their weighted and unweighted datasets to verify its effectiveness.     

网络科学中统一混合理论模型的若干研究进展

复杂网络的理论模型研究一直是网络科学的最重要课题之一.首先概述网络科学理论发展史上的3个里程碑以及有权演化网络的发展概况.为了全面反映确定性与随机性混合的真实世界的统一性、多样性和复杂性,使网络理论模型更加接近实际网络的全面特性,着重评述近年来发展的统一混合网络理论模型的3部曲:和谐混合择优模型、统一混合网络模型和统一混合变速增长网络模型,总结和评述了混合理论模型3部曲的不同特点和相互联系,揭示了统一混合网络的复杂性与普适性及其错综复杂的转变关系.最后指出, 该理论在多层次高科技网络等实际网络中的应用前景.      

Modeling Topology and Nonlinear Dynamical Behavior of the Weighted Scale-Free Networks

An improved weighted scale-free network, which has two evolution mechanisms: topological growth and strength dynamics, has been introduced. The topology structure of the model will be explored in details in this work. The evolution driven mechanism of Olami-Feder-Christensen (OFC) model is added to our model to study the self-organized criticality and the dynamical behavior. We also consider attack mechanism and the study of the model with attack is also investigated in this paper. We find there are differences between the model with attack and without attack.     

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 besorted 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 epidemicmodels on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.     

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.     

中国铁路客运网网络性质的研究

中国铁路客运系统可以采用两种不同的网络构建方式来描述. 一种是以铁路的站点作为“节点”，并以轨道作为“边”，这样生成的网络称为铁路地理网. 统计显示该网络的平均群聚系数〈C〉近似为零，故该网络为树状网络. 另一种是以站点作为“节点”，任意两个站点间只要有同一列车在这两个站点停靠，就可以认为这两个站点间有连线，这样生成的网络称为车流网. 统计显示该网络有较大的平均群聚系数和较小的平均网络距离〈d〉，而且该网络节点的度分布基本上服从无标度幂律分布，故车流网为具有无标度性质的小世界网络. 关键词： 铁路地理网 车流网 小世界 无标度分布     

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.     

Evolution of IPv6 Internet topology with unusual sudden changes

The evolution of Internet topology is not always smooth but sometimes with unusual sudden changes. Consequently, identifying patterns of unusual topology evolution is critical for Internet topology modeling and simulation. We analyze IPv6 Internet topology evolution in IP-level graph to demonstrate how it changes in uncommon ways to restructure the Internet. After evaluating the changes of average degree, average path length, and some other metrics over time, we find that in the case of a large-scale growing the Internet becomes more robust; whereas in a top-bottom connection enhancement the Internet maintains its efficiency with links largely decreased.     

Degree distribution of a scale-free random graph model

In this paper, we consider the degree distribution of a general random graph with multiple edges and loops from the perspective of probability. Based on the first-passage probability of Markov chains, we give a new and rigorous proof to the existence of the network degree distribution and obtain the precise expression of the degree distribution. The analytical results are in good agreement with numerical simulations.     

Markov chain-based degree distributions of evolving networks

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.