Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution （i.e., the scale-free distribution） and random distribution etc.     

Evolution of Traffic Flow with Scale-Free Topology

We investigate the emergence of scale-free behaviour in a traffic system by using the NaSch model to simulate the evolution of traffic flow. A kind of evolution networks has been proposed, which is based on the evolution of the traffic flow. The network growth does not take into account preferential attachment, and the attachment of new node is independent of degree. The simulation results demonstrate that the output distribution of links is well described by a scale-free distribution.     

Phase transition in evolution of traffic flow with scale-free property

This paper investigates the behaviour of traffic flow in traffic systems with a new model based on the NaSch model and cluster approximation of mean-field theory. The proposed model aims at constructing a mapping relationship between the microcosmic behaviour and the macroscopic property of traffic flow. Results demonstrate that scale-free phenomenon of the evolution network becomes obvious when the density value of traffic flow reaches at the critical point of phase transition from free flow to traffic congestion, and jamming is limited in this scale-free structure.     

Evolving model of weighted networks inspired by scientific collaboration networks

Inspired by scientific collaboration networks (SCN), especially our empirical analysis of econophysicists network, an evolutionary model for weighted networks is proposed. Besides a new vertex added in at every time step, old vertices can also attempt to build up new links, or to reconnect the existing links. The number of connections repeated between two nodes is converted into the weight of the link. This provides a natural way for the evolution of link weight. The path-dependent preferential attachment mechanism with local information is also introduced. It increases the clustering coefficient of the network significantly. The model shows the scale-free phenomena in degree and vertex weight distribution. It also gives well qualitatively consistent behavior with the empirical results.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in nongrowth random networks.In this model,we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it.The network evolves according to a vertex strength preferential selection mechanism.During the evolution process,the network always holds its total number of vertices and its total number of single-edges constantly.We show analytically and numerically that a network will form steady scale-free distributions with our model.The results show that a weighted non-growth random network can evolve into scale-free state.It is interesting that the network also obtains the character of an exponential edge weight distribution.Namely,coexistence of scale-free distribution and exponential distribution emerges.     

A self-consistent approach to measure preferential attachment in networks and its application to an inherent structure network

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment rule using time-dependent data. Model networks are grown with known preferential attachment rules to test the method, which is seen to be robust. The method is then applied to a scale-free inherent structure (IS) network, which represents the connections between minima via transition states on a potential energy landscape. Even though this network is static, we can examine the growth of the network as a function of a threshold energy (rather than time), where only those transition states with energies lower than the threshold energy contribute to the network. For these networks we are able to detect the presence of preferential attachment, and this helps to explain the ubiquity of funnels on potential energy landscapes. However, the scale-free degree distribution shows some differences from that of a model network grown using the obtained preferential attachment rules, implying that other factors are also important in the growth process.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.     

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.     

Evolution of network from node division and generation

Aimed at lowering the effect of `rich get richer' in scale-free networks with the Barab\'{a}si and Albert model, this paper proposes a new evolving mechanism, which includes dividing and preference attachment for the growth of a network. A broad scale characteristic which is independent of the initial network topology is obtained with the proposed model. By simulating, it is found that preferential attachment causes the appearance of the scale-free characteristic, while the dividing will decrease the power-law behaviour and drive the evolution of broad scale networks.     

Scale-free networks via attaching to random neighbors

Preferential attachment is considered one of the key factors in the formation of scale-free networks. However, complete random attachment without a preferential mechanism can also generate scale-free networks in nature, such as protein interaction networks in cells. This article presents a new scale-free network model that applies the following general mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach to random neighbors of random vertices that are already well connected. The proposed model does not require global-based preferential strategies and utilizes only the random attachment method. Theoretical analysis and numerical simulation results denote that the proposed model has steady scale-free network characteristics, and random attachment without a preferential mechanism may generate scale-free networks.     

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.     

The emergence of scale-free networks with a seceding mechanism

In order to explore further the underlying mechanism of scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new nodes, the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we obtain an analytical expression of the power-law degree distribution with scaling exponent γ ranging from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results.     

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.     

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     

Predicting the growth of new links by new preferential attachment similarity indices

By revisiting the preferential attachment (PA) mechanism for generating a classical scale-free network, we propose a class of novel preferential attachment similarity indices for predicting future links in evolving networks. Extensive experiments on 14 real-life networks show that these new indices can provide more accurate prediction than the traditional one. Due to the improved prediction accuracy and low computational complexity, these proposed preferential attachment indices can be helpful for providing both instructions for mining unknown links and new insights to understand the underlying mechanisms that drive the network evolution.     

Optimal traffic networks topology: A complex networks perspective

We investigate and analyse an optimal traffic network structure for resisting traffic congestion with different volumes of traffic. For this aim, we introduce a cost function and user-equilibrium assignment (UE) which ensures the flow balance on traffic systems. Our finding is that an optimal network is strongly dependent on the total system flow. And the random network is most desirable when the system flow is small. But for the larger volume of traffic, the network with power-law degree distribution is the optimal one. Further study indicates, for scale-free networks, that the degree distribution exponent has large effects on the congestion of traffic network. Therefore, the volume of traffic and characteristic of network determine the optimal network structure so as to minimize the side-effect produced by traffic congestion.     

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。     

Characterizing traffic time series based on complex network theory

A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series.     

Global forward-predicting dynamic routing for traffic concurrency space stereo multi-layer scale-free network

Many real communication networks, such as oceanic monitoring network and land environment observation network,can be described as space stereo multi-layer structure, and the traffic in these networks is concurrent. Understanding how traffic dynamics depend on these real communication networks and finding an effective routing strategy that can fit the circumstance of traffic concurrency and enhance the network performance are necessary. In this light, we propose a traffic model for space stereo multi-layer complex network and introduce two kinds of global forward-predicting dynamic routing strategies, global forward-predicting hybrid minimum queue(HMQ) routing strategy and global forward-predicting hybrid minimum degree and queue(HMDQ) routing strategy, for traffic concurrency space stereo multi-layer scale-free networks. By applying forward-predicting strategy, the proposed routing strategies achieve better performances in traffic concurrency space stereo multi-layer scale-free networks. Compared with the efficient routing strategy and global dynamic routing strategy, HMDQ and HMQ routing strategies can optimize the traffic distribution, alleviate the number of congested packets effectively and reach much higher network capacity.     

有倾向性重连产生的反匹配网络

在具有网络结构的系统中度关联属性对于动力学行为具有重要的影响, 所以产生适当度关联网络的方法对于大量网络系统的研究具有重要的作用. 尽管产生正匹配网络的方法已经得到很好的验证, 但是产生反匹配网络的方法还没有被系统的讨论过. 重新连接网络中的边是产生度关联网络的一个常用方法. 这里我们研究使用重连方法产生反匹配无标度网络的有效性. 我们的研究表明, 有倾向的重连可以增强网络的反匹配属性. 但是有倾向重连不能使皮尔森度相关系数下降到-1, 而是存在一个依赖于网络参数的最小值. 我们研究了网络的主要参数对于网络度相关系数的影响, 包括网络尺寸, 网络的连接密度和网络节点的度差异程度. 研究表明在网络尺寸大的情况下和节点度差异性强的情况下, 重连的效果较差. 我们研究了真实Internet网络, 发现模型产生的网络经过重连不能达到真实网络的度关联系数.