Fluctuation of the Download Network

The scaling behaviour of fluctuation for a download network we investigated a few years ago based upon Zhang＇s Econophysics web page is presented. A power law scaling, namely σ～〈f〉^α exists between the dispersion a and average flux 〈f〉 of the download rates. The fluctuation exponent α is neither 1/2 nor 1, which were claimed as two universal fluctuation classes in previous publication, while it varies from 1/2 to 1 with the time window in which the download data are accumulated. The crossover behaviour of fluctuation exponents can be qualitatively understood by the external driving fluctuation model for a small-size system or a network traffic model which suggests congestion as the origin.     

Analysis of the airport network of India as a complex weighted network

Transportation infrastructure of a country is one of the most important indicators of its economic growth. Here we study the Airport Network of India (ANI) which represents India’s domestic civil aviation infrastructure as a complex network. We find that ANI, a network of domestic airports connected by air links, is a small-world network characterized by a truncated power-law degree distribution and has a signature of hierarchy. We investigate ANI as a weighted network to explore its various properties and compare them with their topological counterparts. The traffic in ANI, as in the World-wide Airport Network (WAN), is found to be accumulated on interconnected groups of airports and is concentrated between large airports. In contrast to WAN, ANI is found to be having disassortative mixing which is offset by the traffic dynamics. The analysis indicates possible mechanism of formation of a national transportation network, which is different from that on a global scale.     

Jamming transition in air transportation networks

In this work we present a model of an air transportation traffic system from the complex network modelling viewpoint. In the network, every node corresponds to a given airport, and two nodes are connected by means of flight routes. Each node is weighted according to its load capacity, and links are weighted according to the Euclidean distance that separates each pair of nodes. Local rules describing the behaviour of individual nodes in terms of the surrounding flow have been also modelled, and a random network topology has been chosen in a baseline approach. Numerical simulations describing the diffusion of a given number of agents (aircraft) in this network show the onset of a jamming transition that distinguishes an efficient regime with null amount of airport queues and high diffusivity (free phase) and a regime where bottlenecks suddenly take place, leading to a poor aircraft diffusion (congested phase). Fluctuations are maximal around the congestion threshold, suggesting that the transition is critical. We then proceed by exploring the robustness of our results in neutral random topologies by embedding the model in heterogeneous networks. Specifically, we make use of the European air transportation network formed by 858 airports and 11 170 flight routes connecting them, which we show to be scale-free. The jamming transition is also observed in this case. These results and methodologies may introduce relevant decision-making procedures in order to optimize the air transportation traffic.     

Traffic dynamics based on a traffic awareness routing strategy on scale-free networks

By incorporating local traffic information into the shortest path routing strategy, we numerically investigate the effectiveness of the traffic awareness routing strategy for scale-free networks with different clustering. In order to characterize the efficiency of the packet-delivery process, we introduce an order parameter and an average transmission time that allow us to measure the network capacity by the critical value of phase transition from free flow to congestion. Compared with the shortest path routing protocol, the network capacity is greatly enhanced by the traffic awareness routing strategy. We also find that there exists an optimum value for the tunable parameter in the congestion awareness strategy. Moreover, simulation results show that the more clustered the network, the less efficient the packet-delivery process.     

An optimal network for passenger traffic

The optimal solution of an inter-city passenger transport network has been studied using Zipf’s law for the city populations and the Gravity law describing the fluxes of inter-city passenger traffic. Assuming a fixed value for the cost of transport per person per kilometer we observe that while the total traffic cost decreases, the total wiring cost increases with the density of links. As a result the total cost to maintain the traffic distribution is optimal at a certain link density which vanishes on increasing the network size. At a finite link density the network is scale-free. Using this model the air-route network of India has been generated and an one-to-one comparison of the nodal degree values with the real network has been made.     

A complex network model based on the Gnutella protocol

Gnutella is one of the basic protocols for P2P software. In this paper, a novel network model based on Gnutella is introduced. The mechanism of this network is based on resource occupancy and search activities of peers. As for the structure, the power-law exponent of in-degree γ_in≈4.2, the length of the average shortest path 〈l〉=57.74, and the diameter of the network is 156; these topological properties of the proposed structure differ from known results.     

基于预期流优化的空间网络引力模型

从优化预期流的角度提出了一个空间网络模型,其构建目标是使得整个网络的预期流总和最大化.通过改变表征网络对节点适应度和对地理因素依赖程度的两个参数α和γ的取值,网络的拓扑可从异质的星形类网络逐渐演变成同质的类似道路网的网络.利用所提出的引力模型仿真了中国城市航空网,并将其统计特征与实际网络进行了比较.最后,讨论了预期流和实际流（网络中实际的边权）之间的关系. 关键词： 空间网络 预期流 引力 中国城市航空网     

Information traffic in scale-free networks with fluctuations in packet generation rate

We study the information traffic in scale-free networks where the information generation rate varies with time as a periodic function. We observe that when the fluctuation in packet generation rate increases, the average transit time increases and network performance degrades. In order to improve the transportation efficiency in this situation, we propose a new routing method called mixed routing. It operates in two modes: (1) when the packet generation rate is small, the shortest paths are used to deliver the packets to the destination; (2) when the packet generation rate is large, the traffic loads in central nodes are redistributed to other non-central nodes, using the so-called efficient routing method. We find that the time shifting between the two modes is very critical for the routing performance. Consequently, we provide an efficient method to determine the critical times to shift the routing modes for achieving good network performance.     

Universal power laws in the threshold network model: A theoretical analysis based on extreme value theory

We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a theoretical understanding of the distribution of independent and identically distributed random variables within a sufficiently high range. Specifically, the distribution could be generally expressed by a generalized Pareto distribution, which enabled us to formulate the generic weight distribution function. By using the theorem, we obtained the exact expressions of degree distribution and clustering coefficient which behaved as universal power laws within certain ranges of degrees. We also compared the theoretical predictions with numerical results and found that they were extremely consistent.     

A unified model for Sierpinski networks with scale-free scaling and small-world effect

In this paper, we propose an evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Z.Z. Zhang, S.G. Zhou, T. Zou, L.C. Chen, J.H. Guan, Eur. Phys. J. B 60 (2007) 259] and random Sierpinski network [Z.Z. Zhang, S.G. Zhou, Z. Su, T. Zou, J.H. Guan, Eur. Phys. J. B 65 (2008) 141] to the same framework. We suggest an iterative algorithm generating the ESNs. On the basis of the algorithm, some relevant properties of presented networks are calculated or predicted analytically. Analytical solution shows that the networks under consideration follow a power-law degree distribution, with the distribution exponent continuously tuned in a wide range. The obtained accurate expression of clustering coefficient, together with the prediction of average path length reveals that the ESNs possess small-world effect. All our theoretical results are successfully contrasted by numerical simulations. Moreover, the evolutionary prisoner’s dilemma game is also studied on some limitations of the ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.     

Interpersonal interactions and human dynamics in a large social network

We study a large social network consisting of over 10⁶ individuals, who form an Internet community and organize themselves in groups of different sizes. On the basis of the users’ list of friends and other data registered in the database we investigate the structure and time development of the network. The structure of this friendship network is very similar to the structure of different social networks. However, here a degree distribution exhibiting two scaling regimes, power-law for low connectivity and exponential for large connectivity, was found. The groups size distribution and distribution of number of groups of an individual have power-law form. We found very interesting scaling laws concerning human dynamics. Our research has shown how long people are interested in a single task.     

A weighted network evolution with traffic flow

In this paper, we propose a simple weighted network model that generalizes the complex network model evolution with traffic flow previously presented to investigate the relationship between traffic flow and network structure. In the model, the nodes in the network are represented by the traffic flow states, the links in the network are represented by the transform of the traffic flow states, and the traffic flow transported when performing the transform of the traffic flow states is considered as the weight of the link. Several topological features of this generalized weighted model, such as the degree distribution and strength distribution, have been numerically studied. A scaling behavior between the strength and degree s∼klogk is obtained. By introducing some constraints to the generalized weighted model, we study its subnetworks and find that the scaling behavior between the strength and degree is conserved, though the topology properties are quite sensitive to the constraints.     

Opinion formation in a social network: The role of human activity

The model of opinion formation in human population based on social impact theory is investigated numerically. On the basis of a database received from the on-line game server, we examine the structure of social network and human dynamics. We calculate the activity of individuals, i.e. the relative time devoted daily to interactions with others in the artificial society. We study the influence of correlation between the activity of an individual and its connectivity on the process of opinion formation. We find that such correlations have a significant influence on the temperature of the phase transition and the effect of the mass media, modeled as an external stimulation acting on the social network.     

Travel and tourism: Into a complex network

It is discussed how the worldwide tourist arrivals, about 10% of the world’s domestic product, form a largely heterogeneous and directed complex network. Remarkably the random network of connectivity is converted into a scale-free network of intensities. The importance of weights on network connections is brought into discussion. It is also shown how strategic positioning particularly benefits from market diversity and that interactions among countries prevail on a technological and economic pattern, questioning the backbone of driving forces in traveling.     

Heterogeneous distribution of metabolites across plant species

We investigate the distribution of flavonoids, a major category of plant secondary metabolites, across species. Flavonoids are known to show high species specificity, and were once considered as chemical markers for understanding adaptive evolution and characterization of living organisms. We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved among several families: the power-law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid. In order to explain the possible origin of the heterogeneity, we propose a simple model with, essentially, a single parameter. As a result, we show that two respective power-law statistics emerge from simple evolutionary mechanisms based on a multiplicative process. These findings provide insights into the evolution of metabolite diversity and characterization of living organisms that defy genome sequence analysis for different reasons.     

Growing networks with preferential deletion and addition of edges

A preferential attachment model for a growing network incorporating the deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t=1,2,…, with probability π₁>0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π₂ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability π₃=1−π₁−π₂<1/2 a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction p_k of vertices with degree k, and solving this recursion reveals that, for π₃<1/3, we have p_k∼k^{−(3−7π₃)/(1−3π₃)}, while, for π₃>1/3, the fraction p_k decays exponentially at rate (π₁+π₂)/2π₃. There is hence a non-trivial upper bound for how much deletion the network can incorporate without losing the power-law behavior of the degree distribution. The analytical results are supported by simulations.     

A tree-like complex network model

We propose a new tree-like network model. Our results indicate that the tree-like model has a small-world effect with a small average path length and large clustering coefficient. Strikingly, our tree-like model is scale-free. We also add weight to the links following the network structure. With this adding-weight method, the weight of the nodes shows exponential growth, which is ubiquitous in social networks.     

English and Chinese languages as weighted complex networks

In this paper, we analyze statistical properties of English and Chinese written human language within the framework of weighted complex networks. The two language networks are based on an English novel and a Chinese biography, respectively, and both of the networks are constructed in the same way. By comparing the intensity and density of connections between the two networks, we find that high weight connections in Chinese language networks prevail more than those in English language networks. Furthermore, some of the topological and weighted quantities are compared. The results display some differences in the structural organizations between the two language networks. These observations indicate that the two languages may have different linguistic mechanisms and different combinatorial natures.     

A local-world node deleting evolving network model

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting.     

Complex Behaviour for the Origin and Destination Matrix Estimation Problem

The origin and destination （O-D） matrix estimation is an important problem in traffic networks. We apply the gravitation model to express the preference attachment and to analyse the statistical characteristics of the traffic flow in each O-D pair in theory. It is found that the distribution of the future O-D matrix decays as a power law. Additionally, different exponents are obtained for both the constant and variable link cost.