Showing papers in "Physica A-statistical Mechanics and Its Applications in 2016"

Identifying influential spreaders in complex networks based on gravity formula

Abstract: How to identify the influential spreaders in social networks is crucial for accelerating/hindering information diffusion, increasing product exposure, controlling diseases and rumors, and so on. In this paper, by viewing the k-shell value of each node as its mass and the shortest path distance between two nodes as their distance, then inspired by the idea of the gravity formula, we propose a gravity centrality index to identify the influential spreaders in complex networks. The comparison between the gravity centrality index and some well-known centralities, such as degree centrality, betweenness centrality, closeness centrality, and k-shell centrality, and so forth, indicates that our method can effectively identify the influential spreaders in real networks as well as synthetic networks. We also use the classical Susceptible–Infected–Recovered (SIR) epidemic model to verify the good performance of our method.

Stability analysis solutions for nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a magnetized electron–positron plasma

Abstract: The nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov ​(mKdV–ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in magnetized electron–positron plasma which consists of equal hot and cool components of each species. By using the reductive perturbation procedure leads to a mKdV–ZK equation governing the oblique propagation of nonlinear electrostatic modes. The stability of solitary traveling wave solutions of the mKdV–ZK equation to three-dimensional long-wavelength perturbations is investigated. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mKdV–ZK equation. The solutions for the mKdV–ZK equation are obtained precisely and efficiency of the method can be demonstrated.

Chaos synchronization of fractional chaotic maps based on the stability condition

Abstract: In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann–Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method’s effectiveness and fractional chaotic map’s potential role for secure communication.

Evolutionary features of academic articles co-keyword network and keywords co-occurrence network: Based on two-mode affiliation network

Abstract: Keeping abreast of trends in the articles and rapidly grasping a body of article’s key points and relationship from a holistic perspective is a new challenge in both literature research and text mining. As the important component, keywords can present the core idea of the academic article. Usually, articles on a single theme or area could share one or some same keywords, and we can analyze topological features and evolution of the articles co-keyword networks and keywords co-occurrence networks to realize the in-depth analysis of the articles. This paper seeks to integrate statistics, text mining, complex networks and visualization to analyze all of the academic articles on one given theme, complex network(s). All 5944 “complex networks” articles that were published between 1990 and 2013 and are available on the Web of Science are extracted. Based on the two-mode affiliation network theory, a new frontier of complex networks, we constructed two different networks, one taking the articles as nodes, the co-keyword relationships as edges and the quantity of co-keywords as the weight to construct articles co-keyword network, and another taking the articles’ keywords as nodes, the co-occurrence relationships as edges and the quantity of simultaneous co-occurrences as the weight to construct keyword co-occurrence network. An integrated method for analyzing the topological features and evolution of the articles co-keyword network and keywords co-occurrence networks is proposed, and we also defined a new function to measure the innovation coefficient of the articles in annual level. This paper provides a useful tool and process for successfully achieving in-depth analysis and rapid understanding of the trends and relationships of articles in a holistic perspective.

Complex interdependent supply chain networks: Cascading failure and robustness

Abstract: A supply chain network is a typical interdependent network composed of an undirected cyber-layer network and a directed physical-layer network. To analyze the robustness of this complex interdependent supply chain network when it suffers from disruption events that can cause nodes to fail, we use a cascading failure process that focuses on load propagation. We consider load propagation via connectivity links as node failure spreads through one layer of an interdependent network, and we develop a priority redistribution strategy for failed loads subject to flow constraint. Using a giant component function and a one-to-one directed interdependence relation between nodes in a cyber-layer network and physical-layer network, we construct time-varied functional equations to quantify the dynamic process of failed loads propagation in an interdependent network. Finally, we conduct a numerical simulation for two cases, i.e., single node removal and multiple node removal at the initial disruption. The simulation results show that when we increase the number of removed nodes in an interdependent supply chain network its robustness undergoes a first-order discontinuous phase transition, and that even removing a small number of nodes will cause it to crash.

Effect of forward looking sites on a multi-phase lattice hydrodynamic model

Abstract: A new multi-phase lattice hydrodynamic traffic flow model is proposed by considering the effect of multi-forward looking sites on a unidirectional highway. We examined the qualitative properties of proposed model through linear as well as nonlinear stability analysis. It is shown that the multi-anticipation effect can significantly enlarge the stability region on the phase diagram and exhibit three-phase traffic flow. It is also observed that the multi-forward looking sites have prominent influence on traffic flow when driver senses the relative flux of leading vehicles. Theoretical findings are verified using numerical simulation which confirms that the traffic jam is suppressed efficiently by considering the information of leading vehicles in unidirectional multi-phase traffic flow.

Tensor based missing traffic data completion with spatial–temporal correlation

Abstract: Missing and suspicious traffic data is a major problem for intelligent transportation system, which adversely affects a diverse variety of transportation applications. Several missing traffic data imputation methods had been proposed in the last decade. It is still an open problem of how to make full use of spatial information from upstream/downstream detectors to improve imputing performance. In this paper, a tensor based method considering the full spatial–temporal information of traffic flow, is proposed to fuse the traffic flow data from multiple detecting locations. The traffic flow data is reconstructed in a 4-way tensor pattern, and the low-n-rank tensor completion algorithm is applied to impute missing data. This novel approach not only fully utilizes the spatial information from neighboring locations, but also can impute missing data in different locations under a unified framework. Experiments demonstrate that the proposed method achieves a better imputation performance than the method without spatial information. The experimental results show that the proposed method can address the extreme case where the data of a long period of one or several weeks are completely missing.

Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving

Abstract: In a mini-review Kerner (2013) it has been shown that classical traffic flow theories and models failed to explain empirical traffic breakdown — a phase transition from metastable free flow to synchronized flow at highway bottlenecks. The main objective of this mini-review is to study the consequence of this failure of classical traffic-flow theories for an analysis of empirical stochastic highway capacity as well as for the effect of automatic driving vehicles and cooperative driving on traffic flow. To reach this goal, we show a deep connection between the understanding of empirical stochastic highway capacity and a reliable analysis of automatic driving vehicles in traffic flow. With the use of simulations in the framework of three-phase traffic theory, a probabilistic analysis of the effect of automatic driving vehicles on a mixture traffic flow consisting of a random distribution of automatic driving and manual driving vehicles has been made. We have found that the parameters of automatic driving vehicles can either decrease or increase the probability of the breakdown. The increase in the probability of traffic breakdown, i.e., the deterioration of the performance of the traffic system can occur already at a small percentage (about 5%) of automatic driving vehicles. The increase in the probability of traffic breakdown through automatic driving vehicles can be realized, even if any platoon of automatic driving vehicles satisfies condition for string stability.

Evaluating the importance of nodes in complex networks

Abstract: Evaluating the importance of nodes for complex networks is of great significance to the research of survivability and robusticity of networks. This paper proposes an effective ranking method based on degree value and the importance of lines. It can well identify the importance of bridge nodes with lower computational complexity. Firstly, the properties of nodes that are connected to a line are used to compute the importance of the line. Then, the contribution of nodes to the importance of lines is calculated. Finally, degree of nodes and the contribution of nodes to the importance of lines are considered to rank the importance of nodes. Five real networks are used as test data. The experimental results show that our method can effectively evaluate the importance of nodes for complex networks.

Identify influential spreaders in complex networks, the role of neighborhood

Abstract: Identifying the most influential spreaders is an important issue in controlling the spreading processes in complex networks. Centrality measures are used to rank node influence in a spreading dynamics. Here we propose a node influence measure based on the centrality of a node and its neighbors’ centrality, which we call the neighborhood centrality. By simulating the spreading processes in six real-world networks, we find that the neighborhood centrality greatly outperforms the basic centrality of a node such as the degree and coreness in ranking node influence and identifying the most influential spreaders. Interestingly, we discover a saturation effect in considering the neighborhood of a node, which is not the case of the larger the better. Specifically speaking, considering the 2-step neighborhood of nodes is a good choice that balances the cost and performance. If further step of neighborhood is taken into consideration, there is no obvious improvement and even decrease in the ranking performance. The saturation effect may be informative for studies that make use of the local structure of a node to determine its importance in the network.

Multifractal methodology

Abstract: Various methods have been developed independently to study the multifractality of measures in many different contexts Although they all convey the same intuitive idea of giving a "dimension" to sets where a quantity scales similarly within a space, they are not necessarily equivalent on a more rigorous level This review article aims at unifying the multifractal methodology by presenting the multifractal theoretical framework and principal practical methods, namely the moment method, the histogram method, multifractal detrended fluctuation analysis (MDFA) and modulus maxima wavelet transform (MMWT), with a comparative and interpretative eye

Link prediction with node clustering coefficient

Abstract: Predicting missing links in incomplete complex networks efficiently and accurately is still a challenging problem. The recently proposed Cannistrai–Alanis–Ravai (CAR) index shows the power of local link/triangle information in improving link-prediction accuracy. Inspired by the idea of employing local link/triangle information, we propose a new similarity index with more local structure information. In our method, local link/triangle structure information can be conveyed by clustering coefficient of common-neighbors directly. The reason why clustering coefficient has good effectiveness in estimating the contribution of a common-neighbor is that it employs links existing between neighbors of a common-neighbor and these links have the same structural position with the candidate link to this common-neighbor. In our experiments, three estimators: precision, AUP and AUC are used to evaluate the accuracy of link prediction algorithms. Experimental results on ten tested networks drawn from various fields show that our new index is more effective in predicting missing links than CAR index, especially for networks with low correlation between number of common-neighbors and number of links between common-neighbors.

Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks

Abstract: We study the effects of an autapse, which is mathematically described as a self-feedback loop, on the propagation of weak, localized pacemaker activity across a Newman–Watts small-world network consisting of stochastic Hodgkin–Huxley neurons. We consider that only the pacemaker neuron, which is stimulated by a subthreshold periodic signal, has an electrical autapse that is characterized by a coupling strength and a delay time. We focus on the impact of the coupling strength, the network structure, the properties of the weak periodic stimulus, and the properties of the autapse on the transmission of localized pacemaker activity. Obtained results indicate the existence of optimal channel noise intensity for the propagation of the localized rhythm. Under optimal conditions, the autapse can significantly improve the propagation of pacemaker activity, but only for a specific range of the autaptic coupling strength. Moreover, the autaptic delay time has to be equal to the intrinsic oscillation period of the Hodgkin–Huxley neuron or its integer multiples. We analyze the inter-spike interval histogram and show that the autapse enhances or suppresses the propagation of the localized rhythm by increasing or decreasing the phase locking between the spiking of the pacemaker neuron and the weak periodic signal. In particular, when the autaptic delay time is equal to the intrinsic period of oscillations an optimal phase locking takes place, resulting in a dominant time scale of the spiking activity. We also investigate the effects of the network structure and the coupling strength on the propagation of pacemaker activity. We find that there exist an optimal coupling strength and an optimal network structure that together warrant an optimal propagation of the localized rhythm.

Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay

Abstract: Based on the stability theory of fractional-order systems, synchronization of general fractional-order uncertain complex networks with delay is investigated in this paper. By the inequality of the fractional derivative and the comparison principle of the linear fractional equation with delay, synchronization of complex networks with delay is realized under adaptive control. Some sufficient criteria ensuring local asymptotical synchronization under adaptive control and global asymptotical synchronization under adaptive pinning control are derived, respectively. Finally, numerical simulations are presented to demonstrate the validity and feasibility of the proposed synchronization criteria.

Modeling diffusive transport with a fractional derivative without singular kernel

Abstract: In this paper we present an alternative representation of the diffusion equation and the diffusion–advection equation using the fractional calculus approach, the spatial-time derivatives are approximated using the fractional definition recently introduced by Caputo and Fabrizio in the range β , γ ∈ ( 0 ; 2 ] for the space and time domain respectively. In this representation two auxiliary parameters σ x and σ t are introduced, these parameters related to equation results in a fractal space–time geometry provide an entire new family of solutions for the diffusion processes. The numerical results showed different behaviors when compared with classical model solutions. In the range β , γ ∈ ( 0 ; 1 ) , the concentration exhibits the non-Markovian Levy flights and the subdiffusion phenomena; when β = γ = 1 the classical case is recovered; when β , γ ∈ ( 1 ; 2 ] the concentration exhibits the Markovian Levy flights and the superdiffusion phenomena; finally when β = γ = 2 the concentration is anomalous dispersive and we found ballistic diffusion.

Measuring mixing patterns in complex networks by Spearman rank correlation coefficient

Abstract: In this paper, we utilize Spearman rank correlation coefficient to measure mixing patterns in complex networks. Compared with the widely used Pearson coefficient, Spearman coefficient is rank-based, nonparametric, and size-independent. Thus it is more effective to assess linking patterns of diverse networks, especially for large-size networks. We demonstrate this point by testing a variety of empirical and artificial networks. Moreover, we show that normalized Spearman ranks of stubs are subject to an interesting linear rule where the correlation coefficient is just the Spearman coefficient. This compelling linear relationship allows us to directly produce networks with any prescribed Spearman coefficient. Our method apparently has an edge over the well known uncorrelated configuration model.

Analysis of car-following model with cascade compensation strategy

Abstract: Cascade compensation mechanism was designed to improve the dynamical performance of traffic flow system. Two compensation methods were used to study unit step response in time domain and frequency characteristics with different parameters. The overshoot and phase margins are proportional to the compensation parameter in an underdamped condition. Through the comparison we choose the phase-lead compensation method as the main strategy in suppressing the traffic jam. The simulations were conducted under two boundary conditions to verify the validity of the compensator. The conclusion can be drawn that the stability of the system is strengthened with increased phase-lead compensation parameter. Moreover, the numerical simulation results are in good agreement with analytical results.

Fast ranking influential nodes in complex networks using a k-shell iteration factor

Abstract: Identifying the influential nodes of complex networks is important for optimizing the network structure or efficiently disseminating information through networks. The k-shell method is a widely used node ranking method that has inherent advantages in performance and efficiency. However, the iteration information produced in k-shell decomposition has been neglected in node ranking. This paper presents a fast ranking method to evaluate the influence capability of nodes using a k-shell iteration factor. The experimental results with respect to monotonicity, correctness and efficiency have demonstrated that the proposed method can yield excellent performance on artificial and real world networks. It discriminates the influence capability of nodes more accurately and provides a more reasonable ranking list than previous methods.

A modified weighted TOPSIS to identify influential nodes in complex networks

Abstract: Identifying influential nodes in complex networks is still an open issue. Although various centrality measures have been proposed to address this problem, such as degree, betweenness, and closeness centralities, they all have some limitations. Recently, technique for order performance by similarity to ideal solution (TOPSIS), as a tradeoff between the existing metrics, has been proposed to rank nodes effectively and efficiently. It regards the centrality measures as the multi-attribute of the complex network and connects the multi-attribute to synthesize the evaluation of node importance of each node. However, each attribute plays an equally important part in this method, which is not reasonable. In this paper, we improve the method to ranking the node’s spreading ability. A new method, named as weighted technique for order performance by similarity to ideal solution (weighted TOPSIS) is proposed. In our method, we not only consider different centrality measures as the multi-attribute to the network, but also propose a new algorithm to calculate the weight of each attribute. To evaluate the performance of our method, we use the Susceptible–Infected–Recovered (SIR) model to do the simulation on four real networks. The experiments on four real networks show that the proposed method can rank the spreading ability of nodes more accurately than the original method.

Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone

Abstract: In this paper, the impact of the 2008 financial crisis on the weak-form efficiency of twelve Eurozone stock markets is investigated empirically. Efficiency is tested via the Generalized Hurst Exponent method, while dynamic Hurst exponents are estimated by means of the rolling window technique. To account for biases associated with the finite sample size and the leptokurtosis of the financial data, the statistical significance of the Hurst exponent estimates is assessed through a series of Monte-Carlo simulations drawn from the class of α-stable distributions. According to our results, the 2008 crisis has adversely affected stock price efficiency in most of the Eurozone capital markets, leading to the emergence of significant mean-reverting patterns in stock price movements.

Effective leadership for crowd evacuation

Abstract: Evacuation leaders (individuals guiding the crowd) can make crowd evacuation more efficient. Selecting their number and positions within the crowd is particularly important when the other evacuees are not familiar with the internal layout of the building. This paper investigates the effects of leadership on crowd evacuation in rooms with limited visibility range by an extended social force model. We find that, (i) For a large evacuees crowd, a small proportion of the evacuation leaders is already sufficient to guide the whole crowd efficiently, even if the visibility range of the room is very limited. And the smaller the crowd size, the larger the proportion of the leaders is needed to achieve a satisfactory evacuation guidance. (ii) The optimal proportion or number (i.e., the proportion or number that is necessary for guiding the crowd) of the leaders in an evacuees crowd to achieve a satisfactory guidance is related to the visibility range of the room and the distribution range of the evacuees crowd. (iii) Leadership is not always positive to the crowd evacuation. It may have a negative effect on crowd evacuation when the visibility range of the room and the size of the evacuees crowd are large enough. The findings provide a new insight into the effects of leadership on crowd evacuation.

Optimal network topology for structural robustness based on natural connectivity

Abstract: The structural robustness of the infrastructure of various real-life systems, which can be represented by networks, is of great importance. Thus we have proposed a tabu search algorithm to optimize the structural robustness of a given network by rewiring the links and fixing the node degrees. The objective of our algorithm is to maximize a new structural robustness measure, natural connectivity, which provides a sensitive and reliable measure of the structural robustness of complex networks and has lower computation complexity. We initially applied this method to several networks with different degree distributions for contrast analysis and investigated the basic properties of the optimal network. We discovered that the optimal network based on the power-law degree distribution exhibits a roughly “eggplant-like” topology, where there is a cluster of high-degree nodes at the head and other low-degree nodes scattered across the body of “eggplant”. Additionally, the cost to rewire links in practical applications is considered; therefore, we optimized this method by employing the assortative rewiring strategy and validated its efficiency.

Network-based recommendation algorithms: A review

Abstract: Recommender systems are a vital tool that helps us to overcome the information overload problem. They are being used by most e-commerce web sites and attract the interest of a broad scientific community. A recommender system uses data on users’ past preferences to choose new items that might be appreciated by a given individual user. While many approaches to recommendation exist, the approach based on a network representation of the input data has gained considerable attention in the past. We review here a broad range of network-based recommendation algorithms and for the first time compare their performance on three distinct real datasets. We present recommendation topics that go beyond the mere question of which algorithm to use–such as the possible influence of recommendation on the evolution of systems that use it–and finally discuss open research directions and challenges.

Improving interdependent networks robustness by adding connectivity links

Abstract: Compared with a single and isolated network, interdependent networks have two types of links: connectivity link and dependency link. This paper aims to improve the robustness of interdependent networks by adding connectivity links. Firstly, interdependent networks failure model and four frequently used link addition strategies are briefly reviewed. Furthermore, by defining inter degree–degree difference, two novel link addition strategies are proposed. Finally, we verify the effectiveness of our proposed link addition strategies by comparing with the current link addition strategies in three different network models. The simulation results show that, given the number of added links, link allocation strategies have great effects on the robustness of interdependent networks, i.e., the double-network link allocation strategy is superior to single-network link allocation strategy. Link addition strategies proposed in this paper excel the current strategies, especially for BA interdependent networks. Moreover, our work can provide guidance on how to allocate limited resources to an existing interdependent networks system and optimize its topology to avoid the potential cascade failures.

Selfishness- and Selflessness-based models of pedestrian room evacuation

Abstract: Some pedestrian evacuation studies have employed game strategy to deal with moving conflicts involving two or three pedestrians. However, most of these have simply presented game strategies for pedestrians without analyzing the reasons why they choose to defect or cooperate. We believe that selfish and selfless behaviors are two main factors that should be considered in evacuation. In addition to these behaviors, human emotions such as sympathy and behaviors such as vying were also taken into account to investigate their impacts on pedestrians’ strategies. Moreover, an essential objective factor, the building design factor of door width was tested and analyzed. Experimental results showed that the sense of self leads to more defectors and a longer evacuation time. However, sympathy does some good, leading to more cooperators and a shorter evacuation time. Moreover, the exit door width is an essential factor of the evacuation efficiency. When the width was less than 6 cells in a rectangular room with a size greater than 50 × 50, the evacuation time greatly decreased when the width increased. However, this effect was less obvious when the width increased.

Daily happiness and stock returns: Some international evidence

Abstract: In this paper, we examine the relations between the daily happiness sentiment extracted from Twitter and the stock market performance in 11 international stock markets By partitioning this happiness sentiment into quintiles from the least to the happiest days, we first show that the contemporary correlation coefficients between happiness sentiment and index return in the 4 and most-happiness subgroups are higher than that in least, 2 and 3-happiness subgroups Secondly, the happiness sentiment can provide additional explanatory power for index return in the most-happiness subgroup Thirdly, the daily happiness can granger-cause the changes in index return for the majority of stock markets Fourthly, we find that the index return and the range-based volatility of the most-happiness subgroup are larger than those of other subgroups These results highlight the important role of social media in stock market

An experimental study of the “faster-is-slower” effect using mice under panic

Abstract: A number of crowd accidents in last decades have attracted the interests of scientists in the study of self-organized behavior of crowd under extreme conditions. The faster-is-slower effect is one of the most referenced behaviors in pedestrian dynamics. However, this behavior has not been experimentally verified yet. A series of experiments with mice under panic were conducted in a bi-dimensional space. The mice were trained to be familiar with the way of escape. A varying number of joss sticks were used to produce different levels of stimulus to drive the mice to escape. The evacuation process was video-recorded for further analysis. The experiment found that the escape times significantly increased with the levels of stimulus due to the stronger competition of selfish mice in panic condition. The faster-is-slower effect was experimentally verified. The probability distributions of time intervals showed a power law and the burst sizes exhibited an exponential behavior.

A multi-agent genetic algorithm for community detection in complex networks

Abstract: Complex networks are popularly used to represent a lot of practical systems in the domains of biology and sociology, and the structure of community is one of the most important network attributes which has received an enormous amount of attention. Community detection is the process of discovering the community structure hidden in complex networks, and modularity Q is one of the best known quality functions measuring the quality of communities of networks. In this paper, a multi-agent genetic algorithm, named as MAGA-Net, is proposed to optimize modularity value for the community detection. An agent, coded by a division of a network, represents a candidate solution. All agents live in a lattice-like environment, with each agent fixed on a lattice point. A series of operators are designed, namely split and merging based neighborhood competition operator, hybrid neighborhood crossover, adaptive mutation and self-learning operator, to increase modularity value. In the experiments, the performance of MAGA-Net is validated on both well-known real-world benchmark networks and large-scale synthetic LFR networks with 5000 nodes. The systematic comparisons with GA-Net and Meme-Net show that MAGA-Net outperforms these two algorithms, and can detect communities with high speed, accuracy and stability.

An improved Cellular Automata model to simulate the behavior of high density crowd and validation by experimental data

Abstract: In this article we present an improved version of the Cellular Automata floor field model making use of a sub-mesh system to increase the maximum density allowed during simulation and reproduce phenomena observed in dense crowds. In order to calibrate the model’s parameters and to validate it we used data obtained from an empirical observation of bidirectional pedestrian flow. A good agreement was found between numerical simulation and experimental data and, in particular, the double outflow peak observed during the formation of deadlocks could be reproduced in numerical simulations, thus allowing the analysis of deadlock formation and dissolution. Finally, we used the developed high density model to compute the flow-ratio dependent fundamental diagram of bidirectional flow, demonstrating the instability of balanced flow and predicting the bidirectional flow behavior at very high densities. The model we presented here can be used to prevent dense crowd accidents in the future and to investigate the dynamics of the accidents which already occurred in the past. Additionally, fields such as granular and active matter physics may benefit from the developed framework to study different collective phenomena.

Exploring dynamic property of traffic flow time series in multi-states based on complex networks: Phase space reconstruction versus visibility graph

Abstract: A new method based on complex network theory is proposed to analyze traffic flow time series in different states. We use the data collected from loop detectors on freeway to establish traffic flow model and classify the flow into three states based on K-means method. We then introduced two widely used methods to convert time series into networks: phase space reconstruction and visibility graph. Furthermore, in phase space reconstruction, we discuss how to determine delay time constant and embedding dimension and how to select optimal critical threshold in terms of cumulative degree distribution. In the visibility graph, we design a method to construct network from multi-variables time series based on logical OR. Finally, we study and compare the statistic features of the networks converted from original traffic time series in three states based on phase space and visibility by using the degree distribution, network structure, correlation of the cluster coefficient to betweenness and degree–degree correlation.