The Quantitative Law of Network Information Growth

Based on the assumptions of ＂information transfer＂ and ＂information creation＂, this paper educes the multiplied growth mechanism of network information： that the gross quantity of network information （Im） is about n times as much as the quantity of real network information （Ir）. According to this theoretical model, we give a uniform explanation to all kinds of information growth models in existence, and put forward some proposals, such as ＂forbidding information transfer＂ and ＂building up the central information base＂, to control the repeated information flooding on the network and facilitate the full use of network information.

NEW METHOD TO ESTIMATE SCALING EXPONENTS OF POWER-LAW DEGREE DISTRIBUTION AND HIERARCHICAL CLUSTERING FUNCTION FOR COMPLEX NETWORKS

A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS （Kolmogorov-Smirnov） test statistics for 10 CNN （Connecting Nearest-Neighbor） networks.

Performance Evaluation and Pseudo-Conservation Laws in Token Ring Network with Batch Arrivals and Limited Services

This paper,using pseudo-conservation laws in cyclic-service systems, derives some expressions for the weighted sum of the mean waiting time token ring networks with exhaustive limitedservice policies on condition that messages arrived with batch Poisson, and discusses boundary conditions. At the same time, the results of the token ring network with exhaustive and non-exhaustiveservice strategy are obtained. Finally the exact expression of mean waiting time in symmetric ringnetwork with same service strategy is given.

An Analytical Model of the Power Law Distributions in the Complex Network

It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.

Mobile user forecast and power-law acceleration invariance of scale-free networks

This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.

Habits on Social Networks at Workplace: A Survey of Motivations and Behaviour

This article explores the use of social networks by workers in Abidjan, Côte d’Ivoire, with particular emphasis on a descriptive or quantitative analysis aimed at understanding motivations and methods of use. More than five hundred and fifty questionnaires were distributed, highlighting workers’ preferred digital channels and platforms. The results indicate that the majority use social media through their mobile phones, with WhatsApp being the most popular app, followed by Facebook and LinkedIn. The study reveals that workers use social media for entertainment purposes and to develop professional and social relationships, with 55% unable to live without social media at work for recreational activities. In addition, 35% spend on average 1 to 2 hours on social networks, mainly between 12 p.m. and 2 p.m. It also appears that 46% believe that social networks moderately improve their productivity. These findings can guide marketing strategies, training, technology development and government policies related to the use of social media in the workplace.

A new local-world evolving network model

In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen （LC model）. In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.

An estimation formula for the average path length of scale-free networks

A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, N, as the only parameter, two parameters including N and a second parameter α are included in our formula. The parameter α is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.

S-curve networks and an approximate method for estimating degree distributions of complex networks

In the study of complex networks almost all theoretical models have the property of infinite growth, but the size of actual networks is finite. According to statistics from the China Internet IPv4 （Internet Protocol version 4） addresses, this paper proposes a forecasting model by using S curve （logistic curve）. The growing trend of IPv4 addresses in China is forecasted. There are some reference values for optimizing the distribution of IPv4 address resource and the development of IPv6. Based on the laws of IPv4 growth, that is, the bulk growth and the finitely growing limit, it proposes a finite network model with a bulk growth. The model is said to be an S-curve network. Analysis demonstrates that the analytic method based on uniform distributions （i.e., Barabasi-Albert method） is not suitable for the network. It develops an approximate method to predict the growth dynamics of the individual nodes, and uses this to calculate analytically the degree distribution and the scaling exponents. The analytical result agrees with the simulation well, obeying an approximately power-law form. This method can overcome a shortcoming of Barabasi-Albert method commonly used in current network research.

Fluctuations in airport arrival and departure traffic:A network analysis

Air traffic is a typical complex system, in which movements of traffic components （pilots, controllers, equipment, and environment）, especially airport arrival and departure traffic, form complicated spatial and temporal dynamics. The fluctuations of airport arrival and departure traffic are studied from the point of view of networks as the special correlation between different airports. Our collected flow volume data on the time-dependent activity of US airport arrival and departure traffic indicate that the coupling between the average flux and the fluctuation of an individual airport obeys a certain scaling law with a wide variety of scaling exponents between 1/2 and 1. These scaling phenomena can explain the interaction between the airport internal dynamics （e.g. queuing at airports, a ground delay program and following flying traffic） and a change in the external （network-wide） traffic demand （e.g. an increase in traffic during peak hours every day）, allowing us to further understand the mechanisms governing the collective behaviour of the transportation system. We separate internal dynamics from external fluctuations using a scaling law which is helpful for us to systematically determine the origin of fluctuations in airport arrival and departure traffic, uncovering the collective dynamics. Hot spot features are observed in airport traffic data as the dynamical inhomogeneity in the fluxes of individual airports. The intrinsic characteristics of airport arrival and departure traffic under severe weather is discussed as well.

MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.

Modeling online social networks based on preferential linking

We study the phenomena of preferential linking in a large-scale evolving online social network and find that the linear preference holds for preferential creation, preferential acceptance, and preferential attachment. Based on the linear preference, we propose an analyzable model, which illustrates the mechanism of network growth and reproduces the process of network evolution. Our simulations demonstrate that the degree distribution of the network produced by the model is in good agreement with that of the real network. This work provides a possible bridge between the micro=mechanisms of network growth and the macrostructures of online social networks.

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.

Discontinuous Galerkin Method for Macroscopic Traffic Flow Models on Networks

In this paper,we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads.On individual roads,we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters.To solve traffic flows on networks,we construct suitable numerical fluxes at junctions based on preferences of the drivers.We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments,including a junction with complicated traffic light patterns with multiple phases.Differences with the approach to numerical fluxes at junctions fromČanićet al.(J Sci Comput 63:233-255,2015)are discussed and demonstrated numerically on a simple network.

Convergence speed of consensus problems over undirected scale-free networks

Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the influence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions.

THE STUDY ON DEGREE DISTRIBUTION PROPERTY OF COMPLEX NETWORK BASED ON COOPERATIVE COMMUNICATION

Complex networks have been widely studied. Recently,many results show that the degree distributions of some large networks follow the form of power-law and these networks possess better robustness against random nodes failure. As an effective technology on combating the channel fading,wireless cooperative communication is becoming one of the most important methods to improve the wireless communication performances. In this paper,the complex network models based on cooperative communication and non-cooperative communication are established; and the degree distribution properties for them are studied. The simulation results show that the degree distributions of these networks also follow the form of power-law,which means that the addition of cooperative communi-cation links will not change the property of degree distribution and then these networks will possess better robustness against random nodes failure as well.

网络刑法的发展回溯与理论供源

传统刑法体系遭遇网络犯罪形态后频现应答疲态,预防性立法由此显身,开启由网络犯罪策动刑法转型的号角,但网络刑法的理论根基尚不稳。网络刑法的演进是网络社会发展与网络犯罪迸发共同作用下真实的渐显;网络空间社会思维是网络刑法的建构基石,衍生丰富的刑法学意义。网络安全秩序价值的相对优位与网络自由的并重、网络安全法益的统领地位与刑法任务变更、预防性理念的内在觉醒与审慎运行,是网络刑法的根基之本,框定网络刑法的发展脉络。刑法知识迁移是渐进的,网络犯罪、网络归责、网络制裁堪当生成网络刑法知识范畴的参照性“母版”,未来可创设网络刑法典以实现知识结构的创造性立法固化。

Scale-Free Behavior in Weighted Stock Network

A weighted stock network model of stock market is presented based on the complex network theory. The model is a weighted random network, in which each vertex denotes a stock, and the weight assigned to each edge is the cross-correlation coefficient of returns. Analysis of A shares listed at Shanghai Stock Exchange finds that the influence-strength （IS） follows a power-law distribution with the exponent of 2.58. The empirical analysis results show that there are a few stocks whose price fluctuations can powerfully influence the price dynamics of other stocks in the same market. Further econometric analysis reveals that there are significant differences between the positive IS and the negative IS.

Logistic Mapping-Based Complex Network Modeling

In this paper, a new topological approach for studying an integer sequence constructed from Logistic mapping is proposed. By evenly segmenting [0,1]?into N non-overlapping subintervals which is marked as , representing the nodes identities, a network is constructed for analysis. Wherein the undirected edges symbolize their relation of adjacency in an integer sequence obtained from the Logistic mapping and the top integral function. By observation, we find that nodes’ degree changes with different values of??instead of the initial value—X0, and the degree distribution presents the characteristics of scale free network, presenting power law distribution. The results presented in this paper provide some insight into degree distribution of the network constructed from integer sequence that may help better understanding of the nature of Logistic mapping.

Modelling Accelerating Growth with Intermittent Processes in Evolving Networks

In this paper,the acceleratingly growing network model with intermittent processes is proposed.In thegrowing network,there exist both accelerating and intermittent processes.The network is grown from the number ofnodes mo and the number of links added with each new node is a nonlinearly increasing function m+aNβ（t）f（t）,whereN（t） is the number of nodes present at time t.f（t） is the periodic and bistable function with period T,whose values are1 and 0 indicating accelerating and intermittent processes,respectively.Here we denote the ratio r of acceleration timeto whole one.We study the degree distribution p（k） of the model,focusing on the dependence of p（k） on the networkparameters τ,T,m,α,N,and β.It is found that there exists a phase transition point,kc such that if k【kc,then p（k）obeys a power-law distribution with exponent -γ1,while if k】kc,then p（k） exhibits a power-law distribution withexponent-γ2.Moreover,the exponents γ1 and γ2 are independent of τ,T,m,a,and N,while they depend only onthe parameter β.More interesting,the phase transition point is described by kc=aNβ,which is equal to the value atwhich p（k） is maximum in GM model.