Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory

Size: px
Start display at page:

Download "Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory"

Transcription

1 Open Phys. 2017; 15:1 11 Research Article Open Access Xu Zhang* and Bingzhi Chen Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory DOI /phys Received Dec 01, 2016; accepted Dec 27, 2016 Abstract: Complex Network Theory can analyze the reliability of high-speed passenger traffic networks and also evaluate node importance. This paper conducts a systematic and in-depth research of importance of various nodes in the high-speed passenger traffic network so as to improve the high-speed passenger traffic network level. To study importance of network nodes can contribute to an in-depth understanding of the network structure. Therefore, the complex network is introduced and the node importance is evaluated. The characteristics of the complex network are briefly analyzed. In order to study the highspeed passenger traffic nodes, the network restraint coefficient, the network scale, the efficiency, the grade level, the partial clustering coefficient of degree and structural hole. Besides, the algorithm to calculate node importance is designed. Through analysis of the high-speed passenger network, the accuracy and practicability of the Complex Network Theory in evaluating node importance are pointed out. It is also proved that Complex Network Theory can help optimize high-speed passenger traffic networks and improve traffic efficiency. Keywords: high speed passenger transport, complex network, structural hole, node importance, multiple-attribute decision PACS: *Corresponding Author: Xu Zhang: School of Traffic and ransportation Engineering, Dalian Jiaotong University, Dalian , China; @163.com Bingzhi Chen: School of Traffic and ransportation Engineering, Dalian Jiaotong University, Dalian , China; chenbingzhi06@hotmail.com 1 Introduction Development of high-speed passenger traffic is the key to a country s prosperity and a symbol of a country s national comprehensive strength. In recent years, highspeed passenger traffic has entered a leapfrog developmental period, thus contributing to increasing improvement of the high-speed network. Therefore, it has been a research focus to study the complex high-speed network so as to guarantee reliability invulnerability of the complex network. Research suggests that networks of different topological structures show different degrees of invulnerability towards different methods. Compared with the stochastic network, the scale-free network has a higher degree of robustness towards stochastic, but is vulnerable towards a calculated attack. Combination of robustness and vulnerability this is one of the many basic and important characteristics of the complex network. Thus, it is necessary to find key nodes. In this way, not only can the reliability of the whole network be improved through protection of key nodes, but also the high-speed passenger network system can be scientifically evaluated, thus providing suggestions for maintenance and optimization of the network system, and bases for macroscopic decisionmaking of the whole high-speed network system. Foreign scholars have studied the complex network for a long time [1], having put forward the WS model and the BA model [2], and revealing the small-world effect and the scale-free attribute of the complex network [3, 4]. All these have provided a brand-new perspective for network development [5, 6]. Later, the complex network analysis was introduced to multiple fields, including mathematics and sciences [7, 8], life science and engineering science. Now, it has become a major analysis method of network research. The traffic network has significant time and space complexity, and bears most characteristics of the complex network [9]. Study on the traffic network based on the Complex Network Theory and Mechanism has drawn attention of an increasing number of scholars [10]. Based on analysis of topological attributes of the 2017 X. Zhang and B. Chen, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

2 2 X. Zhang and B. Chen real traffic network [11], researchers have verified that the traffic network, the railway network, the urban traffic network and the civil aviation network are all typical complex networks. Based on the node deletion method, the node shrinkage method and the importance evaluation matrix, researchers have also ranked importance of traffic complex network nodes. However, most of them analyzed node importance from the perspective of a singular characteristic index of the traffic network, but ignored interplay among multiple attributes and characteristics. In view of this research gap, this paper applies the Structural Hole Theory to importance analysis of China s high-speed passenger traffic network nodes, and ranks node importance based on multiple attributes and characteristics. 2 Basis model of the complex network 2.1 Small-world network model In 1998, in order to realize the transition from the completely regular network to the completely stochastic network, two American scholars, Watts and Strogatz, designed a small-world network with a small average path length and a large clustering coefficient, and called it WS small-world network model. Below is the construction algorithm of the SW smallworld network model: (1) Start from the regular network: Assume that there is a nearest-neighbor coupling network with N nodes, and that the nodes form a ring. Every node is connected with K/2 nodes near to it on the left and right, and K is an even number; (2) Stochastic reconnection: Stochastically connect to every side of the network with the probability p. In other words, one endpoint of the side is maintained unchanged, and the other end is a node stochastically chosen in the network. It is regulated that there should be one side at most between every two different nodes. Besides, every node cannot be connected with any side. In order to guarantee the sparsity of the network, it is required N K. The network model thus built has a high clustering coefficient. The stochasticized reconnection process greatly reduces the network s average path length, and the network model has a small-world characteristic. When the p value is small, the reconnection process has a slight influence on the network s clustering coefficient. When p = 0, the model is degenerated into a regular network. When p = 1, the model is degenerated into a stochastic network. Through adjustment of the p value, the transition from the completely regular network to the completely stochastic network can be controlled. The clustering coefficient and the average path length of the WS small-world network model can be regarded as the function of reconnection probability, p, which are written as C(p) and L(p), respectively. Within the value scope of certain p, the WS network model can guarantee its short average path length (small-world characteristic) and a high degree of aggregation (high aggregation characteristic). During the stochastic reconnection process of the WS small-world network mode, the network connectivity might be destroyed. In order to avoid isolated subnet caused by reconnection, American scholars, Newman and Watts, put forward the small-world network featuring the stochastic bordering to replace the previous one featuring the stochastic reconnection, and the new one was called the NW small-world network. Below is the construction algorithm of the NW small-world network model: (1) Start from the regular network: Assume that there is a nearest-neighbor coupling network with N nodes, and that the nodes form a ring. Every node is connected with K/2 nodes near to it on the left and right, and K is an even number; (2) Stochastic bordering: Add a side to the middle of a pair of nodes stochastically chosen at the probability of p It is regulated that there should be one side at most between every two different nodes. Besides, every node cannot be connected with any side. When p = 0, the model is degenerated to a regular network; when p = 1, the model is degenerated into a stochastic network. Through adjustment of the p value, the model can be controlled to transit from the completely regular network to the completely stochastic network. (1) Degree of aggregation Degree of aggregation of the WS small-world network [12]: 3(k 2) C(p) = 4(k 1) (1 p)3 (1) Degree of aggregation of the small-world network: C(p) = 3(K 2) 4(K 1) + 4Kp(p + 2) (2) Average path length Up to now, none have obtained an accurate analytical expression for the average path length of the WS small-world network model. Newman, Moore and Watts obtained the following approximate formula through the renormalization method and the sequence expansion method, respectively: (p) = 2N K (2) f (NKP/2) (3)

3 Study on node importance evaluation of the high-speed passenger... 3 Where, f (u) stands for a universal scale function, and meets the following condition [13]: { const u 1 Lf (u) = (4) (ln u)/u u 1 Up to now, there has not yet been an accurate analytical expression for f (u). Based on the mean field method, Newman et al. provided the following approximate expression: f (x) 1 2 x 2 + 2x arctan h x x + 2 (3) Degree distribution In terms of the WS small-world network, when k K/2, then p(k) = min(k K 2, K 2 ) n=0 (pk/2) k K 2 n pk (k K/2 n)! e 2 Cn K/2 (1 p) n p K n 2 When k K/2, P(k) = 0. In terms of the NW smallworld network, the degree of every node should be at least k [14]. Therefore, when k K, the probability of a stochastically chosen node, whose degree is k, is: ( ) k K ( P(k) = C N Kp k K 1 Kp ) N k+k (7) N N When k K, P(k) = 0. To some up, the degree distribution of the ER stochastic network, the WS small-world network and the NW small-world network can be approximately expressed by the Poisson distribution. The distribution has a peak value at the mean value < k > of the degree, and then undergoes rapid exponential decline. The type of networks is called the homogenous network or the exponential network [15]. 2.2 Scale-free network model In recent years, a large number of empirical researches have suggested that the degree distribution function of many large-scale real networks (such as WWW, Internet and metabolism network) all feature the power-law distribution, namely P(k) k γ. In such a network, most nodes have a small degree, but there are some nodes with a large degree and without a characteristic scale. Networks of this type whose node connection degree shows no significant characteristic scale are called scale-free networks. In order to explain the generation mechanism of the power-law distribution in the real network, Barabási and Albert put forward a scale-free network model in 1999, which is called (5) (6) the BA scale-free model. The construction of the model is mainly based on two internal mechanisms of the real network: (1) Growth mechanism: Most real networks are an open system. Along with the passage of time, the network scale keeps expanding. In other words, the number of network nodes and sides keeps on increasing; (2) Preferential connection: The newly-increased nodes prefer to connection with nodes with a higher connection degree [16]. Below is the construction algorithm of the BA scalefree network model: (1) Growth: In the initial moment, it is assumed that there have been m 0 nodes. In every follow-up time step, a node with the connection degree of m(m m 0 ) is increased, and the newly-increased node is connected with m different nodes. There is no repeated connection [17, 18]. (2) Preferential connection: During the selection of the connection point for a new node, the probability of a new node to be connected with an existing node, i, is Π i, which is in direct proportion to the degree, k i, of the node, i. i = k i (8) k j After t steps, the algorithm can generate a network with N = t + m 0 nodes and mt sides [19]. (1) Average path length The average path length of the BA scale-free network: L j log N log log N This indicates that the BA scale-free network also has the small-world characteristic. (2) Coefficient of the aggregation degree Below is the aggregation degree of the BA scale-free network: C = m2 (m + 1) 2 4(m 1) [ ln ( ) m + 1 m ] [ ] 2 1 ln(t) m + 1 t (9) (10) Similar to the ER stochastic network, when the network scale is large enough, the BA scale-free network will show no significant clustering characteristic. (3) Degree distribution There are three approaches to working out the degree distribution of the BA scale-free network: a. Mean-Field Approach; b. Master-Equation Approach; c. Rate-Equation Approach. The approximate results obtained by the three approaches are the same. Among them, results obtained by the Master-Equation Approach and the Rate-Equation Approach are equal in value. Through analytical calculation, 2m(m + 1) P(k) = k(k + 1)(k + 2) 2m2 k 3 (11)

4 4 X. Zhang and B. Chen Table 1: Comparison of attributes of the small-world network, the scale-free network and the real network Comparison Regular Stochastic WS small-world BA scale-free A large number parameters network network network network of real networks Average distance Large Small Large Small Small Aggregation Large Small Large Small Large coeflcient Degree δ function Poisson Exponential Power-law Approximate power-law distribution distribution distribution distribution power-law distribution This suggests that the degree distribution of the BA scale-free network can be approximately described by the power-law function whose power exponent is 3. 3 Selection of indexes to evaluate the network node importance of the high-speed passenger network Based on some indexes of degree and structural hole, such as the network restraint coefficient, the network efficient scale, efficiency and grade, the contribution of various passenger stations towards node importance under constrictions of various indexes is analyzed. 3.1 Network degree 3.2 Network restraint coeflcient A network restraint coefficient is used to evaluate the degree of reliance of one node on other nodes. The higher the network restraint coefficient is, the stronger the restriction is, the smaller the structural hole is and the higher probability for it to become the central node. The degree of constraint is shown below: C ij = (P ij + q P iq P qj ) 2 (13) In the above equation, Node q is the shared neighboring node of Node i and Node j; P ij stands for the proportion intensity of Node j on all connecting nodes of Node I; stands for the indirect investment of Node i on Node j. For example, in the high-speed passenger network, Passenger Station q stands for the shared connection node of Passenger Station I; P ij stands for the proportion of Passenger Station j among all connecting stations of Passenger Station i. The total restraint coefficient of Node i is: The degree of Node i is defined as the number of neighboring nodes of the node. Below is the specific expression: C i = j C ij (14) k i = j G a ij (12) Degree can reflect the degree of direct influence of a node on other nodes. The higher the numerical value is, the more important it is in the network. For example, in a high-speed passenger traffic network, a high-speed passenger station has 50 stations connected with it, then the degree of the high-speed passenger station is 50. Under general conditions, the more the neighboring nodes a high-speed passenger station has, the greater the influence of the high-speed passenger station, the larger its scale is, and the more important the node is. 3.3 Grade Grade is used to describe the concentration degree of node restriction. The higher the grade is, the more likely it is within the scope of the node, and the more likely the restraint concentrates on the node. Below is the calculation formula: ( ) ( ) Cij Cij ln C/N C/N j HI i = (15) N ln N Where, N stands for the number of all nodes; C stands for the restraint coefficient of nodes.

5 Study on node importance evaluation of the high-speed passenger Network scale Network scale is used to describe the general influence of nodes, which can measure the importance of structural hole s nodes to some extent. Below is the calculation formula: ES i = (1 P ip P qj ) = n 1 P n jq (16) j q j q Where, n stands for the degree of Node i; j stands for the neighboring nodes of Node i; q stands for the shared neighboring nodes of Node i and Node j; P ip and P qj stands for the proportion of Node q among the neighboring nodes of Node i and Node j. 3.5 Eflciency Efficiency is used to stand for the degree of influence of nodes on other relevant nodes in the network. Under general conditions, nodes in the structural hole have a higher efficiency. Below is the calculation formula: EF i = ES i n (17) n stands for the number of nodes. When the network is fully connected, the efficiency is 1; otherwise, the efficiency is Local clustering coeflcient Local clustering coefficient can reflect the tendency of station points to form a cluster with the neighboring nodes. Generally speaking, only nodes with a small clustering coefficient might become nodes of the structural hole. Below is the calculation formula: C(i) = 2E(i) k(i)[k(i) 1] (18) Where, E(i) stands for the number of actually existing sides of neighboring sides of Node i; k(i) stands for the degree of Node i. 4 Building of the evaluation model From the perspective of spatial autocorrelation, the nearer the two objects are to each other, the stronger the reliance is between them. Based on the space autocorrelation theory, it is thought that nodes neighboring current nodes contribute more to the importance of the nodes. Existing research has suggested that some characteristics of many complex systems are positively correlated with the degree of the node. Thus, during the node importance evaluation process, the index importance contribution matrix of neighboring nodes is positively correlated with the value of degree. When, the influence of only one characteristic (such as value of degree) on node importance is considered, the node importance evaluation function of Eq. (19) is introduced in terms of any Node i: I i = aδ i + b 1 j π 1 i δ j +b 2 j π 2 i δ j + + b m j π m i δ j (19) Where, I i stands for the importance index of Node i; δ stands for the node attribute value, which can be the degree of node or the network constraint coefficient; a and b are two adjustable parameters, which are used to adjust the degree of reliance of node importance on the node attributes and the neighbouring nodes from the first order to the n th order, respectively. From the perspective of autocorrelation, in order to fully consider the contribution of importance of the node and the neighboring nodes, here the value of a and b meets the conditions of k b > a > b and 1 > b > 0, where k stands for the node s mean degree. From Eq. (19), it can be seen that the evaluation function comprehensively considers the contribution of the node to the importance of the node itself and the neighboring nodes of the m order. Besides, the farther the node is away from Node i, the less contribution it is to the importance of Node i. Considering the influence of neighboring nodes of the m order on node importance, the location information of the node is utilized. For the convenience of understanding, here, neighboring nodes of the m order to be evaluated are regarded as the depth of neighboring nodes to be observed for the node importance evaluation, and their value should meet the condition of D m 0. Generally speaking, in real life, when importance of target objects is evaluated, the influence of multiple factors will be taken into consideration. To network nodes, their importance is not fully decided by their degree and structural hole index. The remaining factors should also be accommodated to so as to achieve an accurate evaluation of node importance. Thus, it is assumed that every node selects n evaluation indexes, and that δ i,j is used to stand for the j index value of Node i. Therefore, the importance evaluation model of Node i can be defined as below: I i = AE i (20) Where, I i stands for the degree of importance of Node i; A stands for the evaluation coefficient matrix or the

6 6 X. Zhang and B. Chen importance degree contribution matrix; E i stands for the contribution of the node itself and its neighboring nodes of various orders to the importance of Node i. Here, it is assumed that neighboring nodes of the same order contribute the same amount to Node i. In other words, their evaluation coefficient is the same. W stands for the evaluation index matrix of Node i, which includes the index value of Node I and various neighboring nodes; W stands for the index weight matrix, which is used to stand for the degree of reliance of the importance of Node i on various indexes. Here, the proportion of the weight of n evaluation indexes is written as, w 1, w 2,, w n. Under the multi-factor situation, the single-factor evaluation function is maintained. The method to calculate the contribution of neighboring nodes of the same order to the importance of Node i is shown below: δ m i,j = δ j,n, (21) j πi m Where, δ m j,n stands for the total contribution amount of the set of neighbouring nodes of the m order belonging to Node i to the importance of Node I under the restriction of the n index; δ j,n (j πi m ) stands for the value of the n index of the central node j among neighboring nodes of the m order belonging to Node I. It is assumed that the value of the n indexes of Node i is {δ i,1, δ i,2, δ i,n }. Therefore, the evaluation index matrix in Eq. (19) can be expressed as below: δ 0 i,1 δ 0 i,2 δ 0 i,n δ 1 i,1 δ 1 i,2 δ 1 i,n E i =.. (22). δ m i,1 δ m i,2 δ m i,n δ i,1 δ i,2 δ i,n δ j,1 δ j,2 δ j,n j π 1 i j π 1 i j π 1 i =... δ j,2 j π m i δ j,1 j π m i j π m i δ j,n The value scope of different indexes might vary greatly. For example, the degree of the same node might be several hundred, but its network restraint coefficient might be smaller than 1. The physical meaning and the measurement unit of various indexes might not necessarily be the same, thus might lead to a different data dimension and magnitude. Therefore, it is necessary to conduct normalization of the evaluation index matrix. From Eq. (21), it can be seen every column of elements corresponds to one index. There are n indexes in total. The following normalization equation is adopted to process every index value: δ k i,j = δ k i,j min δk i,j max δ k i,j min, j = 1, 2,... n (23) δk i,j In order to work out the normalization evaluation index matrix based on the index value after normalization, it is assumed that the importance of any Node i in the network can be expressed a I i = AE iw, namely: δ 0 i,1 δ 0 i,2 δ 0 i,n [ I i = a, b 1, b 2,..., b n] δ 1 i,1 δ 1 i,2 δ 1 i,n.. (24). δ m i,1 δ m i,2 δ m i,n w 1 w 2. w 5 Algorithm flow i π k i Based on comprehensive consideration of contribution of the node itself and nodes of the m order to node importance under restrictions of various indexes, relatively accurate evaluation results can be obtained. To consider the degree value of the node itself is critical to evaluating the importance of the node. To some extent, the value of degree reflects node importance. To accommodate to the information of neighboring nodes of the m th order can help analyze the importance of a node in the whole network and reflects the importance of the node location. The network topology, G = {V, L}, the evaluation index set and the index weight matrix, W, have been already known. Below is the algorithm flow to evaluate node importance: (1) Extract the node set of any Node i according to the network topological institutions πi k ; (2) Calculate every index value of the set of neighboring nodes of various orders belonging to Node i: δ k i,1 = δ i,1, k = 1, 2,..., m, i = 1, 2,.., n and the evaluation index matrix of Node i is E i confirmed; (3) Conduct normalization of indexes of E i to obtain the evaluation index matrix E i after normalization; (4) According to the ideal value of various indexes, bj * (j = 1, 2,..., n) and work out the weighting coefficient of various indexes, wj * (j = 1, 2,..., n); (5) Output the target value of various indexes according to Eq. 24. After the target value of nodes is obtained, the target value is ranked from large ones to small ones. The former

7 Study on node importance evaluation of the high-speed passenger... nodes are much more important than latter nodes. According to the ranking results of the node importance, the node or the node set most important to the network can be confirmed. Based on the above node importance evaluation method, it can be seen that evaluation indexes and neighboring nodes to be observed are the key to the whole evaluation effect. The evaluation process relies on characteristics of nodes, thus ignoring the location information of nodes in the network. The evaluation results are similar to those obtained through the traditional connection degree approach. As to selection of evaluation indexes, the degree and structural hole of nodes is a key to reflecting node importance. Thus, based on the evaluation indexes, the specific evaluation model is built. 7 Figure 1: Topological diagram of civil aviation network Figure 2: Topological diagram of HSR network 6 Case study of evaluating importance of nodes in the high-speed passenger traflc network based on China s high-speed passenger traflc network 6.1 Construction of China s high-speed passenger traflc network While building the high-speed rail and civil aviation compound network, this paper makes the following hypotheses: (1) a high-speed passenger transport network is a complex network built in space p. If there is an airline or a highspeed railway between two cities, then it is considered that two cities have an edge. (2) the high-speed passenger transport network is an undirected weighted network. If a city has a high-speed rail station and an airport simultaneously, then this city is considered as a node. Under the above hypotheses, the operation data of China s high-speed rail and civil aviation in 2015 are statistically analyzed. The data source of the civil aviation subnetwork is the Summer Flight Schedule The database contains 10,093 flights of more than 20 airlines in China (excluding flights to Hong Kong, Macau and Taiwan) and 196 cities. (See the topological diagram of civil aviation network in Fig. 1). The HSR (high-speed rail) data are from operation plans of high-speed trains, bullet trains and intercity railways formulated by the Railways Bureau since Figure 3: Topological diagram of passenger traflc network The network contains about 4,000 high-speed train numbers and 425 high-speed rail stations all over China. (See the topological diagram of HSR network in Fig. 2) Based on relevant data of the civil aviation sub-network and the high-speed rail sub-network, the high-speed passenger traffic network is built. The network contains 579 nodes and 14,312 sides. Refer to Fig. 3 for the topological diagram of high-speed passenger traffic network. 6.2 Importance evaluation of major nodes Based on a comprehensive analysis of the degree, the average path length and the aggregation degree coefficient of China s high-speed passenger traffic network nodes, 15 important nodes are chosen. See below: Beijingv1, Shanghai-v2, Nanjing-v3, Guangzhou-v4, Shenzhenv5, Xiamen-v6, Changsha-v7, Jinan-v8, Chengdu-v9, Hangzhou-v10, Wuhan-v11, Zhengzhou-v12, Nanchangv13, Hefei-v14 and Kunshan-v15. According to Part 4 of this paper, the value of various evaluation indexes of these nodes is shown in Table 2. Table 2 shows the calculation results of every index of nodes: Build the evaluation matrix based on the value of

8 8 X. Zhang and B. Chen Table 2: Value of node evaluation indexes Station Node Network restraint coeflcient Grade Eflcient scale Eflciency Local clustering coeflcient Beijing v Shanghai v Nanjing v Guangzhou v Shenzhen v Xiamen v Changsha v Jinan v Chengdu v Hangzhou v Wuhan v Zhengzhou v Nanchang v Hefei v Kunshan v every index: E i = Conduct normalization of every index: E i = In terms of the matrix, the ideal point is b * = (1, 1, 1, 1, 1, 1, 1). Thus, the index weighting vector of the matrix worked out according to the formula is W * = (0.0859, , , , , ). Calculate the target value of evaluation: d i = (0.9294, , 0.681, , , , , , 0.512, , , , , , ) Table 3 uses the algorithm and the algorithm respectively proposed by Literature [20], Literature [21] and Literature [22] to obtain evaluation results of node importance of the high-speed passenger traffic network. Besides, a = 1 and b = 0.5. The node importance evaluation results obtained by the four algorithms are different, because they have different focuses. The basic idea of the algorithm proposed in this paper is to evaluate importance of various nodes based on various node indexes and the analytic hierarchy process. The algorithm proposed in Literature [20] is based on changes of networks generated after removal of nodes. The algorithm proposed in Literature [21] decides the key nodes based on the capability of nodes to provide the shortest available path of the network. The algorithm proposed in Literature 23 evaluates node importance based on contribution of various nodes to network information transmission in the network. It just accommodates to contribution of nodes to importance of neighboring nodes. Evaluation Results suggest that the algorithm proposed in this paper comes up with the most important

9 Study on node importance evaluation of the high-speed passenger... 9 Table 3: Node importance evaluation based on the algorithm in this paper Node Algorithm proposed Algorithm proposed Algorithm proposed Algorithm proposed in this paper by Literature 20 by Literature 21 by Literature 22 v v v v v v v v v v v v v v v node in the high-speed passenger traffic network, which is v1. From Table 3, it can be seen that the most important node worked out by the algorithm in this paper is v1, which is different from that obtained by the algorithm proposed in Literature [22], but the same to that proposed in Literature [20] and Literature [21]. This suggests the algorithm proposed in this paper is accurate in some way. From the above table, it can be seen that the algorithm based on the network constraint coefficient, efficient scale, efficiency and local clustering coefficient, respectively, the algorithm proposed in Literature [20] (node removal approach) and the algorithm proposed in Literature [21] (the capability of providing the shortest available path) all obtain the most important node to be v1. Among them, the algorithm based on the network coefficient, efficient scale, efficiency and local clustering coefficient belongs to the single-index calculation, thus being limited, low in evaluation accuracy and large in evaluation error. In terms of the node removal approach, if it deletes too many nodes, it will result in network disconnection and failure of accurately evaluating the degree of node importance. The algorithm based on the capability of providing the shortest available path can increase the node evaluation accuracy, but its calculation process is complex and its accuracy is poor in finding the key node. To sum up, the algorithm proposed in this paper comprehensively considers the global importance of nodes, combines the node structural hole attribute and accounts for the structural hole indexes of various aspects of nodes to evaluate the node importance. 6.3 Analysis of algorithm eflciency This paper uses four operation methods, i.e., the proposed algorithm, algorithms involved in References [20, 21] and [22] to evaluate the node importance of the proposed network. The operating time of each algorithm is as shown in Fig. 4. It can be seen from the figure that, with the increase of number of nodes, the slope of the proposed algorithm declines and the time decreases, suggesting that the proposed method is significantly better than the other three methods. So the proposed evaluation method of node importance has a high efficiency and is suitable for the calculation of large-scale complex networks. Algorithm time(s) number of nodes Proposed algorithm References 20 References 21 References 22 Figure 4: Operation hours of different numbers of nodes in the network

10 10 X. Zhang and B. Chen Table 4: High speed passenger transport network node importance degree (descending) results Evaluation algorithms Algorithm based on the network constraint coeflcient Algorithm based on the grade Algorithm based on the eflcient scale Algorithm based on the eflciency Algorithm based on the local clustering coeflcient Algorithm proposed in this paper Algorithm proposed in Literature 20 Algorithm proposed in Literature 21 Algorithm proposed in Literature 22 Node series v1, v2, v11, v10, v3, v13, v4, v7, v14, v12, v15, v8, v9, v6, v5 v5, v9, v4, v6, v13, v12, v8, v14, v15, v2, v1, v7, v3, v10, v11 v1, v2, v4, v10, v3, v5, v11, v7, v9, v6, v13, v8, v15, v12, v14 v1, v2, v4, v11, v10, v13, v3, v9, v7, v8, v15, v6, v12, v14, v5 v1, v2, v11, v10, v3, v13, v4, v7, v12, v14, v15, v8, v9, v6, v5 v1, v2, v4, v10, v3, v5, v11, v7, v9, v6, v13, v8, v15, v12, v14 v1, v2, v4, v5, v3, v11, v10, v7, v13, v9, v6, v8, v15, v14, v12 v1, v2, v9, v4, v10, v5, v3, v11, v7, v12, v6, v15, v13, v8, v14 v2, v1, v5, v4, v3, v10, v9, v7, v11, v6, v13, v15, v8, v12, v14 7 Conclusions Complex Network Theory has vital research value and scope for further research. To apply the theory to traffic analysis can help scholars get an in-depth understanding of the operational rules governing traffic networking systems and help master the complexity of traffic networks both microscopically and macroscopically. This paper mainly introduces basic knowledge of the complex network, the calculation of various indexes of the complex network nodes and the evaluation of node importance. Below is a brief review of the research work in this paper: 1. Analyze the research status of the complex network both at home and abroad based on relevant literatures and research findings, and analyze problems of the complex network in traffic; 2. Briefly introduce the basic theories of the complex network and the structural hole theory, including some indexes to calculate the structural hole node, such as the network constraint coefficient, grade, network scale, efficiency and local clustering coefficient; 3. The complex network is important in that it is a reliable index to measure the traffic network s stability. The influence of some commonly-used measuring indexes of the road network s reliability on nodes is analyzed. 4. Introduce the structural hole indexes and use the multi-attribute decision-making to combine the structural hole and degree to analyze characteristics of different indexes. Analyze the high-speed passenger traffic network based on analysis of concepts of different indexes and approaches to calculate the node importance. 5. Analyze findings and put forward reasonable building plans. The traffic system, either in terms of its topological structure or in terms of its evolution process, has significant complex network characteristics. The combination of the complex network system and the traffic network has good application prospects. Besides, research done in the traffic field can deepen, enrich and expand the Complex Network Theory. The high-speed passenger traffic network is a relatively complex system. Compounded by characteristics of the traffic field, it becomes an even more complex system. Based on the high-speed passenger traffic network, this paper conducts a study on the complex network. The topological structures are analyzed, the extraction and ranking of key nodes are explored and suggestions to optimize key nodes are put forward. However, there are still some problems calling for further research. For example, research on nodes when the path weighting is considered, and the influence of different network structures and network scales on key nodes are the research direction in the future. Acknowledgement: This research was supported by the National Social Science Foundation major research project(no.13&zd170), and LiaoNing Doctoral Scientific Research Foundation(No ). References [1] Erdos P., Renyi A., On the evolution of random graphs, Pub. Math. Inst. Hung. Acad. Sci.1960, 5, [2] Duucan J W., Steven H S., Collective dynamics of small-world networks, Nature, 1998, 393,

11 Study on node importance evaluation of the high-speed passenger [3] Albert L B., Réka A., Emergence of scaling in random networks, Science, 1999, 286, [4] Xu F., Zhu J F.,Yang W D., Construction of High-Speed Railway and Airline and the Analysis of Its Network Topology Compound Network Characteristics, Complex Systems and Complexity Science, 2013, 10, [5] Senp D S., C P A M., Small-world Properties of the Indian rail-way network, Physical Review E, 2003, 67, [6] Re ka A., Hawoong J., Error and attack tolerance of complex networks, Nature, 2000, 406, [7] Zhao W., He H S., Lin Z C., et al., The study of properties of Chinese railway passenger transport network, Acta Phys. Sin, 2006, 55, [8] Richard G. C., Ben P., Miguel R., Likelihood-based assessment of dynamic networks, IMA J Complex Netw, 2016, 4, [9] Liu H K., Zhou T., Empirical study of Chinese city airline network, Acta Phys. Sin, 2007, 56, [10] Yang G Y., Rong Z H., Li., A Survey of Evolutionary Game Theory on Complex Networks, Complex Systems and Complexity Science, 2008, 5, [11] Guan M., Li B., Zhao H., Research and Analysis of Complex Networks Statistical Regularity for Internet, Computer Engineering, 2008, 34, [12] Su K., Wang L F., Zhang Z., Flexible Weighted Complex Network Evolving Model and Simulation, Journal of System Simulation, 2009, 21, [13] Chen L., Chen Z., Li H G., Analysis on the Evolution of Firm s Interpersonal Relationships Network Based on Complex Network, Journal of Shanghai Jiaotong University, 2009, 9, [14] Yang L L., Yang Y C., Crime organization Relation Mining Based on Social Network, Computer Engineering, 2009, 35, [15] Jin J., Xu K., Xiong N., et al., Multi-index evaluation algorithm based on principal component analysis for node importance in complex networks, IETNETWORKS, 2012, 1, [16] Zhang J., Xu X K., Li P., et al., Node importance for dynamical process on networks: a multi scale characterization, Chaos, 2011, 21, [17] Vishwanath B. A., Shankar N., Mahesh K N., Multigrid method for the solution of EHL line contact with bio-based oils as lubricants, Applied Mathematics and Nonlinear Sciences, 2016, 2, [18] Siddu S., Mundewadi R A., Modified Wavelet Full-Approximation Scheme for the Numerical Solution of Nonlinear Volterra integral and integro-differential Equations, Applied Mathematics and Nonlinear Sciences, 2016, 2, [19] F. Marín F A., Solano J., Merono J F., Sánchez. Multi-scale Simulations of Dry Friction Using Network Simulation Method, Applied Mathematics and Nonlinear Sciences, 2016, 2, [20] Chen Y., Hu A Q., Hu X., A Method for Finding the Most Vital Node in Communication Networks, Journal of China Institute of Communications, 2004, 25, [21] Tan Y J., Wu J., Deng H Z., Evaluation Method for Node Importance based on Node Contraction in Complex Networks, Systems Engineering-Theory & Practice, 2006, 11, [22] Zhai Y H., Wang Z L., Zheng J., et al., Finding most vital node by node importance contribution matrix in communication network, Journal of Beijing University of Aeronautics and Astronautics, 2009, 35, [23] Zhang F M., Li K W., et al., Finding vital node by node importance evaluation matrix in complex networks, Acta Phys. Sin.2012, 61,

A study on reliability of high-speed passenger transport network based on complex network analysis 1

A study on reliability of high-speed passenger transport network based on complex network analysis 1 Acta Technica 61 No. 4A/2016), 25 38 c 2017 Institute of Thermomechanics CAS, v.v.i. A study on reliability of high-speed passenger transport network based on complex network analysis 1 Xu Zhang 2, Bingzhi

More information

An Evolving Network Model With Local-World Structure

An Evolving Network Model With Local-World Structure The Eighth International Symposium on Operations Research and Its Applications (ISORA 09) Zhangjiajie, China, September 20 22, 2009 Copyright 2009 ORSC & APORC, pp. 47 423 An Evolving Network odel With

More information

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks Journal of Systems Science and Information Aug., 2017, Vol. 5, No. 4, pp. 367 375 DOI: 10.21078/JSSI-2017-367-09 A New Evaluation Method of Node Importance in Directed Weighted Complex Networks Yu WANG

More information

Statistical analysis of the airport network of Pakistan

Statistical analysis of the airport network of Pakistan PRAMANA c Indian Academy of Sciences Vol. 85, No. 1 journal of July 2015 physics pp. 173 183 Statistical analysis of the airport network of Pakistan YASIR TARIQ MOHMAND, AIHU WANG and HAIBIN CHEN School

More information

Research on Community Structure in Bus Transport Networks

Research on Community Structure in Bus Transport Networks Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 1025 1030 c Chinese Physical Society and IOP Publishing Ltd Vol. 52, No. 6, December 15, 2009 Research on Community Structure in Bus Transport Networks

More information

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 950 954 c International Academic Publishers Vol. 45, No. 5, May 15, 2006 Small World Properties Generated by a New Algorithm Under Same Degree of All

More information

Research on Design and Application of Computer Database Quality Evaluation Model

Research on Design and Application of Computer Database Quality Evaluation Model Research on Design and Application of Computer Database Quality Evaluation Model Abstract Hong Li, Hui Ge Shihezi Radio and TV University, Shihezi 832000, China Computer data quality evaluation is the

More information

Structural Analysis of Paper Citation and Co-Authorship Networks using Network Analysis Techniques

Structural Analysis of Paper Citation and Co-Authorship Networks using Network Analysis Techniques Structural Analysis of Paper Citation and Co-Authorship Networks using Network Analysis Techniques Kouhei Sugiyama, Hiroyuki Ohsaki and Makoto Imase Graduate School of Information Science and Technology,

More information

Road Network Traffic Congestion Evaluation Simulation Model based on Complex Network Chao Luo

Road Network Traffic Congestion Evaluation Simulation Model based on Complex Network Chao Luo 6th International Conference on Machinery, Materials, Environment, Biotechnology and Computer (MMEBC 26) Road Network Traffic Congestion Evaluation Simulation Model based on Complex Network Chao Luo Department

More information

On Complex Dynamical Networks. G. Ron Chen Centre for Chaos Control and Synchronization City University of Hong Kong

On Complex Dynamical Networks. G. Ron Chen Centre for Chaos Control and Synchronization City University of Hong Kong On Complex Dynamical Networks G. Ron Chen Centre for Chaos Control and Synchronization City University of Hong Kong 1 Complex Networks: Some Typical Examples 2 Complex Network Example: Internet (William

More information

Controllability of Complex Power Networks

Controllability of Complex Power Networks Network and Communication Technologies; Vol. 3, No. 1; 018 ISSN 197-064X E-ISSN 197-0658 Published by Canadian Center of Science and Education Controllability of Complex Power Networks Guohua Zhang 1,

More information

Properties of Biological Networks

Properties of Biological Networks Properties of Biological Networks presented by: Ola Hamud June 12, 2013 Supervisor: Prof. Ron Pinter Based on: NETWORK BIOLOGY: UNDERSTANDING THE CELL S FUNCTIONAL ORGANIZATION By Albert-László Barabási

More information

Response Network Emerging from Simple Perturbation

Response Network Emerging from Simple Perturbation Journal of the Korean Physical Society, Vol 44, No 3, March 2004, pp 628 632 Response Network Emerging from Simple Perturbation S-W Son, D-H Kim, Y-Y Ahn and H Jeong Department of Physics, Korea Advanced

More information

Wednesday, March 8, Complex Networks. Presenter: Jirakhom Ruttanavakul. CS 790R, University of Nevada, Reno

Wednesday, March 8, Complex Networks. Presenter: Jirakhom Ruttanavakul. CS 790R, University of Nevada, Reno Wednesday, March 8, 2006 Complex Networks Presenter: Jirakhom Ruttanavakul CS 790R, University of Nevada, Reno Presented Papers Emergence of scaling in random networks, Barabási & Bonabeau (2003) Scale-free

More information

Complex Networks. Structure and Dynamics

Complex Networks. Structure and Dynamics Complex Networks Structure and Dynamics Ying-Cheng Lai Department of Mathematics and Statistics Department of Electrical Engineering Arizona State University Collaborators! Adilson E. Motter, now at Max-Planck

More information

Overlay (and P2P) Networks

Overlay (and P2P) Networks Overlay (and P2P) Networks Part II Recap (Small World, Erdös Rényi model, Duncan Watts Model) Graph Properties Scale Free Networks Preferential Attachment Evolving Copying Navigation in Small World Samu

More information

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv: v1 [physics.soc-ph] 12 May 2008

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv: v1 [physics.soc-ph] 12 May 2008 Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv:0805.1712v1 [physics.soc-ph] 12 May 2008 Keumsook Lee a,b Woo-Sung Jung c Jong Soo Park d M. Y.

More information

STUDY OF THE DEVELOPMENT OF THE STRUCTURE OF THE NETWORK OF SOFIA SUBWAY

STUDY OF THE DEVELOPMENT OF THE STRUCTURE OF THE NETWORK OF SOFIA SUBWAY STUDY OF THE DEVELOPMENT OF THE STRUCTURE OF THE NETWORK OF SOFIA SUBWAY ИЗСЛЕДВАНЕ НА РАЗВИТИЕТО НА СТРУКТУРАТА НА МЕТРОМРЕЖАТА НА СОФИЙСКИЯ МЕТОПОЛИТЕН Assoc. Prof. PhD Stoilova S., MSc. eng. Stoev V.,

More information

(Social) Networks Analysis III. Prof. Dr. Daning Hu Department of Informatics University of Zurich

(Social) Networks Analysis III. Prof. Dr. Daning Hu Department of Informatics University of Zurich (Social) Networks Analysis III Prof. Dr. Daning Hu Department of Informatics University of Zurich Outline Network Topological Analysis Network Models Random Networks Small-World Networks Scale-Free Networks

More information

Characteristics of Preferentially Attached Network Grown from. Small World

Characteristics of Preferentially Attached Network Grown from. Small World Characteristics of Preferentially Attached Network Grown from Small World Seungyoung Lee Graduate School of Innovation and Technology Management, Korea Advanced Institute of Science and Technology, Daejeon

More information

Warship Power System Survivability Evaluation Based on Complex Network Theory Huiying He1,a, Hongjiang Li1, Shaochang Chen1 and Hao Xiong1,2,b

Warship Power System Survivability Evaluation Based on Complex Network Theory Huiying He1,a, Hongjiang Li1, Shaochang Chen1 and Hao Xiong1,2,b International Industrial Informatics and Computer Engineering Conference (IIICEC 05) Warship Power System Survivability Evaluation Based on Complex Network Theory Huiying He,a, Hongjiang Li, Shaochang

More information

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure https://doi.org/10.3991/ijoe.v13i03.6863 Zhigang Zhao Zhejiang University of Media and Communications,

More information

Landslide Monitoring Point Optimization. Deployment Based on Fuzzy Cluster Analysis.

Landslide Monitoring Point Optimization. Deployment Based on Fuzzy Cluster Analysis. Journal of Geoscience and Environment Protection, 2017, 5, 118-122 http://www.scirp.org/journal/gep ISSN Online: 2327-4344 ISSN Print: 2327-4336 Landslide Monitoring Point Optimization Deployment Based

More information

Reliability Analysis for Aviation Airline Network Based on Complex Network

Reliability Analysis for Aviation Airline Network Based on Complex Network doi: 10.5028/jatm.v6i2.295 Reliability Analysis for Aviation Airline Network Based on Complex Network Dong Bing 1,2 ABSTRACT: In order to improve the reliability of aviation airline network, this paper

More information

Attack Vulnerability of Network with Duplication-Divergence Mechanism

Attack Vulnerability of Network with Duplication-Divergence Mechanism Commun. Theor. Phys. (Beijing, China) 48 (2007) pp. 754 758 c International Academic Publishers Vol. 48, No. 4, October 5, 2007 Attack Vulnerability of Network with Duplication-Divergence Mechanism WANG

More information

Pheromone Static Routing Strategy for Complex Networks. Abstract

Pheromone Static Routing Strategy for Complex Networks. Abstract Pheromone Static Routing Strategy for Complex Networks Xiang Ling 1, Henry Y.K. Lau 2, Rui Jiang 1, and Mao-Bin Hu 1 1.School of Engineering Science, University of Science and Technology of China, arxiv:1108.6119v1

More information

A Generating Function Approach to Analyze Random Graphs

A Generating Function Approach to Analyze Random Graphs A Generating Function Approach to Analyze Random Graphs Presented by - Vilas Veeraraghavan Advisor - Dr. Steven Weber Department of Electrical and Computer Engineering Drexel University April 8, 2005 Presentation

More information

Traffic Flow Prediction Based on the location of Big Data. Xijun Zhang, Zhanting Yuan

Traffic Flow Prediction Based on the location of Big Data. Xijun Zhang, Zhanting Yuan 5th International Conference on Civil Engineering and Transportation (ICCET 205) Traffic Flow Prediction Based on the location of Big Data Xijun Zhang, Zhanting Yuan Lanzhou Univ Technol, Coll Elect &

More information

manufacturing process.

manufacturing process. Send Orders for Reprints to reprints@benthamscience.ae The Open Automation and Control Systems Journal, 2014, 6, 203-207 203 Open Access Identifying Method for Key Quality Characteristics in Series-Parallel

More information

The Gene Modular Detection of Random Boolean Networks by Dynamic Characteristics Analysis

The Gene Modular Detection of Random Boolean Networks by Dynamic Characteristics Analysis Journal of Materials, Processing and Design (2017) Vol. 1, Number 1 Clausius Scientific Press, Canada The Gene Modular Detection of Random Boolean Networks by Dynamic Characteristics Analysis Xueyi Bai1,a,

More information

Lesson 4. Random graphs. Sergio Barbarossa. UPC - Barcelona - July 2008

Lesson 4. Random graphs. Sergio Barbarossa. UPC - Barcelona - July 2008 Lesson 4 Random graphs Sergio Barbarossa Graph models 1. Uncorrelated random graph (Erdős, Rényi) N nodes are connected through n edges which are chosen randomly from the possible configurations 2. Binomial

More information

The Research of Delay Characteristics in CAN Bus Networked Control System

The Research of Delay Characteristics in CAN Bus Networked Control System Journal of Computational Information Systems 9: 18 (2013) 7517 7523 Available at http://www.jofcis.com The Research of Delay Characteristics in CAN Bus Networked Control System Yi WANG 1, Liren HE 2, Ming

More information

Modelling weighted networks using connection count

Modelling weighted networks using connection count Home Search Collections Journals About Contact us My IOPscience Modelling weighted networks using connection count This article has been downloaded from IOPscience. Please scroll down to see the full text

More information

Empirical Analysis of the Spread of University Students Amative Behavior

Empirical Analysis of the Spread of University Students Amative Behavior Applied Mathematics, 2013, 4, 137-141 http://dx.doi.org/10.4236/am.2013.48a019 Published Online August 2013 (http://www.scirp.org/journal/am) Empirical Analysis of the Spread of University Students Amative

More information

Failure in Complex Social Networks

Failure in Complex Social Networks Journal of Mathematical Sociology, 33:64 68, 2009 Copyright # Taylor & Francis Group, LLC ISSN: 0022-250X print/1545-5874 online DOI: 10.1080/00222500802536988 Failure in Complex Social Networks Damon

More information

Multi-dimensional database design and implementation of dam safety monitoring system

Multi-dimensional database design and implementation of dam safety monitoring system Water Science and Engineering, Sep. 2008, Vol. 1, No. 3, 112-120 ISSN 1674-2370, http://kkb.hhu.edu.cn, e-mail: wse@hhu.edu.cn Multi-dimensional database design and implementation of dam safety monitoring

More information

Complex networks: A mixture of power-law and Weibull distributions

Complex networks: A mixture of power-law and Weibull distributions Complex networks: A mixture of power-law and Weibull distributions Ke Xu, Liandong Liu, Xiao Liang State Key Laboratory of Software Development Environment Beihang University, Beijing 100191, China Abstract:

More information

Global dynamic routing for scale-free networks

Global dynamic routing for scale-free networks Global dynamic routing for scale-free networks Xiang Ling, Mao-Bin Hu,* Rui Jiang, and Qing-Song Wu School of Engineering Science, University of Science and Technology of China, Hefei 230026, People s

More information

Comprehensive analysis and evaluation of big data for main transformer equipment based on PCA and Apriority

Comprehensive analysis and evaluation of big data for main transformer equipment based on PCA and Apriority IOP Conference Series: Earth and Environmental Science PAPER OPEN ACCESS Comprehensive analysis and evaluation of big data for main transformer equipment based on PCA and Apriority To cite this article:

More information

Volume 2, Issue 11, November 2014 International Journal of Advance Research in Computer Science and Management Studies

Volume 2, Issue 11, November 2014 International Journal of Advance Research in Computer Science and Management Studies Volume 2, Issue 11, November 2014 International Journal of Advance Research in Computer Science and Management Studies Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com

More information

IMPROVED ARTIFICIAL FISH SWARM ALGORITHM AND ITS APPLICATION IN OPTIMAL DESIGN OF TRUSS STRUCTURE

IMPROVED ARTIFICIAL FISH SWARM ALGORITHM AND ITS APPLICATION IN OPTIMAL DESIGN OF TRUSS STRUCTURE IMPROVED ARTIFICIAL FISH SWARM ALGORITHM AD ITS APPLICATIO I OPTIMAL DESIG OF TRUSS STRUCTURE ACAG LI, CHEGUAG BA, SHUJIG ZHOU, SHUAGHOG PEG, XIAOHA ZHAG College of Civil Engineering, Hebei University

More information

Critical Phenomena in Complex Networks

Critical Phenomena in Complex Networks Critical Phenomena in Complex Networks Term essay for Physics 563: Phase Transitions and the Renormalization Group University of Illinois at Urbana-Champaign Vikyath Deviprasad Rao 11 May 2012 Abstract

More information

Advanced Algorithms and Models for Computational Biology -- a machine learning approach

Advanced Algorithms and Models for Computational Biology -- a machine learning approach Advanced Algorithms and Models for Computational Biology -- a machine learning approach Biological Networks & Network Evolution Eric Xing Lecture 22, April 10, 2006 Reading: Molecular Networks Interaction

More information

CSCI5070 Advanced Topics in Social Computing

CSCI5070 Advanced Topics in Social Computing CSCI5070 Advanced Topics in Social Computing Irwin King The Chinese University of Hong Kong king@cse.cuhk.edu.hk!! 2012 All Rights Reserved. Outline Graphs Origins Definition Spectral Properties Type of

More information

Time Series Clustering Ensemble Algorithm Based on Locality Preserving Projection

Time Series Clustering Ensemble Algorithm Based on Locality Preserving Projection Based on Locality Preserving Projection 2 Information & Technology College, Hebei University of Economics & Business, 05006 Shijiazhuang, China E-mail: 92475577@qq.com Xiaoqing Weng Information & Technology

More information

Summary: What We Have Learned So Far

Summary: What We Have Learned So Far Summary: What We Have Learned So Far small-world phenomenon Real-world networks: { Short path lengths High clustering Broad degree distributions, often power laws P (k) k γ Erdös-Renyi model: Short path

More information

NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016

NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016 NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016 Caesar S. Benipayo, PhD Student Under advisement of Dr. Michael Grenn and Dr. Blake Roberts Department of Engineering

More information

Introduction to Networks and Business Intelligence

Introduction to Networks and Business Intelligence Introduction to Networks and Business Intelligence Prof. Dr. Daning Hu Department of Informatics University of Zurich Sep 16th, 2014 Outline n Network Science A Random History n Network Analysis Network

More information

Higher order clustering coecients in Barabasi Albert networks

Higher order clustering coecients in Barabasi Albert networks Physica A 316 (2002) 688 694 www.elsevier.com/locate/physa Higher order clustering coecients in Barabasi Albert networks Agata Fronczak, Janusz A. Ho lyst, Maciej Jedynak, Julian Sienkiewicz Faculty of

More information

Open Access Research on the Prediction Model of Material Cost Based on Data Mining

Open Access Research on the Prediction Model of Material Cost Based on Data Mining Send Orders for Reprints to reprints@benthamscience.ae 1062 The Open Mechanical Engineering Journal, 2015, 9, 1062-1066 Open Access Research on the Prediction Model of Material Cost Based on Data Mining

More information

An improved PageRank algorithm for Social Network User s Influence research Peng Wang, Xue Bo*, Huamin Yang, Shuangzi Sun, Songjiang Li

An improved PageRank algorithm for Social Network User s Influence research Peng Wang, Xue Bo*, Huamin Yang, Shuangzi Sun, Songjiang Li 3rd International Conference on Mechatronics and Industrial Informatics (ICMII 2015) An improved PageRank algorithm for Social Network User s Influence research Peng Wang, Xue Bo*, Huamin Yang, Shuangzi

More information

Introduction to network metrics

Introduction to network metrics Universitat Politècnica de Catalunya Version 0.5 Complex and Social Networks (2018-2019) Master in Innovation and Research in Informatics (MIRI) Instructors Argimiro Arratia, argimiro@cs.upc.edu, http://www.cs.upc.edu/~argimiro/

More information

arxiv:cond-mat/ v1 21 Oct 1999

arxiv:cond-mat/ v1 21 Oct 1999 Emergence of Scaling in Random Networks Albert-László Barabási and Réka Albert Department of Physics, University of Notre-Dame, Notre-Dame, IN 46556 arxiv:cond-mat/9910332 v1 21 Oct 1999 Systems as diverse

More information

Fault Analysis of Distribution Network with Flexible Ring Network Control Device

Fault Analysis of Distribution Network with Flexible Ring Network Control Device 6th International Conference on Advanced Design and Manufacturing Engineering (ICADME 2016) Fault Analysis of Distribution Network with Flexible Ring Network Control Device Kuo Tan 1, a, Chenghong Tang

More information

arxiv:cond-mat/ v1 [cond-mat.dis-nn] 3 Aug 2000

arxiv:cond-mat/ v1 [cond-mat.dis-nn] 3 Aug 2000 Error and attack tolerance of complex networks arxiv:cond-mat/0008064v1 [cond-mat.dis-nn] 3 Aug 2000 Réka Albert, Hawoong Jeong, Albert-László Barabási Department of Physics, University of Notre Dame,

More information

Application of Improved Lzc Algorithm in the Discrimination of Photo and Text ChengJing Ye 1, a, Donghai Zeng 2,b

Application of Improved Lzc Algorithm in the Discrimination of Photo and Text ChengJing Ye 1, a, Donghai Zeng 2,b 2016 International Conference on Information Engineering and Communications Technology (IECT 2016) ISBN: 978-1-60595-375-5 Application of Improved Lzc Algorithm in the Discrimination of Photo and Text

More information

CS-E5740. Complex Networks. Scale-free networks

CS-E5740. Complex Networks. Scale-free networks CS-E5740 Complex Networks Scale-free networks Course outline 1. Introduction (motivation, definitions, etc. ) 2. Static network models: random and small-world networks 3. Growing network models: scale-free

More information

Internet as a Complex Network. Guanrong Chen City University of Hong Kong

Internet as a Complex Network. Guanrong Chen City University of Hong Kong Internet as a Complex Network Guanrong Chen City University of Hong Kong 1 Complex Network: Internet (K. C. Claffy) 2 Another View of the Internet http://www.caida.org/analysis/topology/as_core_network/

More information

Framework Research on Privacy Protection of PHR Owners in Medical Cloud System Based on Aggregation Key Encryption Algorithm

Framework Research on Privacy Protection of PHR Owners in Medical Cloud System Based on Aggregation Key Encryption Algorithm Framework Research on Privacy Protection of PHR Owners in Medical Cloud System Based on Aggregation Key Encryption Algorithm Huiqi Zhao 1,2,3, Yinglong Wang 2,3*, Minglei Shu 2,3 1 Department of Information

More information

Aero-engine PID parameters Optimization based on Adaptive Genetic Algorithm. Yinling Wang, Huacong Li

Aero-engine PID parameters Optimization based on Adaptive Genetic Algorithm. Yinling Wang, Huacong Li International Conference on Applied Science and Engineering Innovation (ASEI 215) Aero-engine PID parameters Optimization based on Adaptive Genetic Algorithm Yinling Wang, Huacong Li School of Power and

More information

Cascading failures in complex networks with community structure

Cascading failures in complex networks with community structure International Journal of Modern Physics C Vol. 25, No. 5 (2014) 1440005 (10 pages) #.c World Scienti c Publishing Company DOI: 10.1142/S0129183114400051 Cascading failures in complex networks with community

More information

Smallest small-world network

Smallest small-world network Smallest small-world network Takashi Nishikawa, 1, * Adilson E. Motter, 1, Ying-Cheng Lai, 1,2 and Frank C. Hoppensteadt 1,2 1 Department of Mathematics, Center for Systems Science and Engineering Research,

More information

Research on Measured Course Accuracy Based on Relative Measure between Azimuth and Relative Bearing

Research on Measured Course Accuracy Based on Relative Measure between Azimuth and Relative Bearing nd International Conference on Education Technology, Management and Humanities Science (ETMHS 016) Research on Measured Course Accuracy Based on Relative Measure etween Azimuth and Relative Bearing Wang

More information

Topologies and Centralities of Replied Networks on Bulletin Board Systems

Topologies and Centralities of Replied Networks on Bulletin Board Systems Topologies and Centralities of Replied Networks on Bulletin Board Systems Qin Sen 1,2 Dai Guanzhong 2 Wang Lin 2 Fan Ming 2 1 Hangzhou Dianzi University, School of Sciences, Hangzhou, 310018, China 2 Northwestern

More information

Impact of Topology on the Performance of Communication Networks

Impact of Topology on the Performance of Communication Networks Impact of Topology on the Performance of Communication Networks Pramode K. Verma School of Electrical & Computer Engineering The University of Oklahoma 4502 E. 41 st Street, Tulsa, Oklahoma 74135, USA

More information

Application of Redundant Backup Technology in Network Security

Application of Redundant Backup Technology in Network Security 2018 2nd International Conference on Systems, Computing, and Applications (SYSTCA 2018) Application of Redundant Backup Technology in Network Security Shuwen Deng1, Siping Hu*, 1, Dianhua Wang1, Limin

More information

Research Article Modeling and Simulation Based on the Hybrid System of Leasing Equipment Optimal Allocation

Research Article Modeling and Simulation Based on the Hybrid System of Leasing Equipment Optimal Allocation Discrete Dynamics in Nature and Society Volume 215, Article ID 459381, 5 pages http://dxdoiorg/11155/215/459381 Research Article Modeling and Simulation Based on the Hybrid System of Leasing Equipment

More information

TCM Health-keeping Proverb English Translation Management Platform based on SQL Server Database

TCM Health-keeping Proverb English Translation Management Platform based on SQL Server Database 2019 2nd International Conference on Computer Science and Advanced Materials (CSAM 2019) TCM Health-keeping Proverb English Translation Management Platform based on SQL Server Database Qiuxia Zeng1, Jianpeng

More information

A Real-time Detection for Traffic Surveillance Video Shaking

A Real-time Detection for Traffic Surveillance Video Shaking International Conference on Mechatronics, Control and Electronic Engineering (MCE 201) A Real-time Detection for Traffic Surveillance Video Shaking Yaoyao Niu Zhenkuan Pan e-mail: 11629830@163.com e-mail:

More information

Adaptive Boundary Effect Processing For Empirical Mode Decomposition Using Template Matching

Adaptive Boundary Effect Processing For Empirical Mode Decomposition Using Template Matching Appl. Math. Inf. Sci. 7, No. 1L, 61-66 (2013) 61 Applied Mathematics & Information Sciences An International Journal Adaptive Boundary Effect Processing For Empirical Mode Decomposition Using Template

More information

A Data Classification Algorithm of Internet of Things Based on Neural Network

A Data Classification Algorithm of Internet of Things Based on Neural Network A Data Classification Algorithm of Internet of Things Based on Neural Network https://doi.org/10.3991/ijoe.v13i09.7587 Zhenjun Li Hunan Radio and TV University, Hunan, China 278060389@qq.com Abstract To

More information

A Training Simulator for PD Detection Personnel

A Training Simulator for PD Detection Personnel Journal of Power and Energy Engineering, 2014, 2, 573-578 Published Online April 2014 in SciRes. http://www.scirp.org/journal/jpee http://dx.doi.org/10.4236/jpee.2014.24077 A Training Simulator for PD

More information

Image segmentation based on gray-level spatial correlation maximum between-cluster variance

Image segmentation based on gray-level spatial correlation maximum between-cluster variance International Symposium on Computers & Informatics (ISCI 05) Image segmentation based on gray-level spatial correlation maximum between-cluster variance Fu Zeng,a, He Jianfeng,b*, Xiang Yan,Cui Rui, Yi

More information

arxiv:cond-mat/ v1 [cond-mat.dis-nn] 14 Sep 2005

arxiv:cond-mat/ v1 [cond-mat.dis-nn] 14 Sep 2005 APS/xxx Load Distribution on Small-world Networks Huijie Yang, Tao Zhou, Wenxu Wang, and Binghong Wang Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of

More information

Universal Behavior of Load Distribution in Scale-free Networks

Universal Behavior of Load Distribution in Scale-free Networks Universal Behavior of Load Distribution in Scale-free Networks K.-I. Goh, B. Kahng, and D. Kim School of Physics and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Korea (February

More information

Improving Suffix Tree Clustering Algorithm for Web Documents

Improving Suffix Tree Clustering Algorithm for Web Documents International Conference on Logistics Engineering, Management and Computer Science (LEMCS 2015) Improving Suffix Tree Clustering Algorithm for Web Documents Yan Zhuang Computer Center East China Normal

More information

Fingerprint Ridge Distance Estimation: Algorithms and the Performance*

Fingerprint Ridge Distance Estimation: Algorithms and the Performance* Fingerprint Ridge Distance Estimation: Algorithms and the Performance* Xiaosi Zhan, Zhaocai Sun, Yilong Yin, and Yayun Chu Computer Department, Fuyan Normal College, 3603, Fuyang, China xiaoszhan@63.net,

More information

The Design and Implementation of Disaster Recovery in Dual-active Cloud Center

The Design and Implementation of Disaster Recovery in Dual-active Cloud Center International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) The Design and Implementation of Disaster Recovery in Dual-active Cloud Center Xiao Chen 1, a, Longjun Zhang

More information

A Low-Overhead Hybrid Routing Algorithm for ZigBee Networks. Zhi Ren, Lihua Tian, Jianling Cao, Jibi Li, Zilong Zhang

A Low-Overhead Hybrid Routing Algorithm for ZigBee Networks. Zhi Ren, Lihua Tian, Jianling Cao, Jibi Li, Zilong Zhang A Low-Overhead Hybrid Routing Algorithm for ZigBee Networks Zhi Ren, Lihua Tian, Jianling Cao, Jibi Li, Zilong Zhang Chongqing Key Lab of Mobile Communications Technology, Chongqing University of Posts

More information

The Establishment of Large Data Mining Platform Based on Cloud Computing. Wei CAI

The Establishment of Large Data Mining Platform Based on Cloud Computing. Wei CAI 2017 International Conference on Electronic, Control, Automation and Mechanical Engineering (ECAME 2017) ISBN: 978-1-60595-523-0 The Establishment of Large Data Mining Platform Based on Cloud Computing

More information

An Improved Method of Vehicle Driving Cycle Construction: A Case Study of Beijing

An Improved Method of Vehicle Driving Cycle Construction: A Case Study of Beijing International Forum on Energy, Environment and Sustainable Development (IFEESD 206) An Improved Method of Vehicle Driving Cycle Construction: A Case Study of Beijing Zhenpo Wang,a, Yang Li,b, Hao Luo,

More information

Selection of Best Web Site by Applying COPRAS-G method Bindu Madhuri.Ch #1, Anand Chandulal.J #2, Padmaja.M #3

Selection of Best Web Site by Applying COPRAS-G method Bindu Madhuri.Ch #1, Anand Chandulal.J #2, Padmaja.M #3 Selection of Best Web Site by Applying COPRAS-G method Bindu Madhuri.Ch #1, Anand Chandulal.J #2, Padmaja.M #3 Department of Computer Science & Engineering, Gitam University, INDIA 1. binducheekati@gmail.com,

More information

Design of Coal Mine Power Supply Monitoring System

Design of Coal Mine Power Supply Monitoring System 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016) Design of Coal Mine Power Supply Monitoring System Lei Shi 1, Guo Jin 2 and Jun Xu 3 1 2 Department of electronic

More information

An Improved DCT Based Color Image Watermarking Scheme Xiangguang Xiong1, a

An Improved DCT Based Color Image Watermarking Scheme Xiangguang Xiong1, a International Symposium on Mechanical Engineering and Material Science (ISMEMS 2016) An Improved DCT Based Color Image Watermarking Scheme Xiangguang Xiong1, a 1 School of Big Data and Computer Science,

More information

Quality Assessment of Power Dispatching Data Based on Improved Cloud Model

Quality Assessment of Power Dispatching Data Based on Improved Cloud Model Quality Assessment of Power Dispatching Based on Improved Cloud Model Zhaoyang Qu, Shaohua Zhou *. School of Information Engineering, Northeast Electric Power University, Jilin, China Abstract. This paper

More information

Design of student information system based on association algorithm and data mining technology. CaiYan, ChenHua

Design of student information system based on association algorithm and data mining technology. CaiYan, ChenHua 5th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering (ICMMCCE 2017) Design of student information system based on association algorithm and data mining technology

More information

Organization and Retrieval Method of Multimodal Point of Interest Data Based on Geo-ontology

Organization and Retrieval Method of Multimodal Point of Interest Data Based on Geo-ontology , pp.49-54 http://dx.doi.org/10.14257/astl.2014.45.10 Organization and Retrieval Method of Multimodal Point of Interest Data Based on Geo-ontology Ying Xia, Shiyan Luo, Xu Zhang, Hae Yong Bae Research

More information

Fault Diagnosis of Wind Turbine Based on ELMD and FCM

Fault Diagnosis of Wind Turbine Based on ELMD and FCM Send Orders for Reprints to reprints@benthamscience.ae 76 The Open Mechanical Engineering Journal, 24, 8, 76-72 Fault Diagnosis of Wind Turbine Based on ELMD and FCM Open Access Xianjin Luo * and Xiumei

More information

Utilizing Restricted Direction Strategy and Binary Heap Technology to Optimize Dijkstra Algorithm in WebGIS

Utilizing Restricted Direction Strategy and Binary Heap Technology to Optimize Dijkstra Algorithm in WebGIS Key Engineering Materials Online: 2009-10-08 ISSN: 1662-9795, Vols. 419-420, pp 557-560 doi:10.4028/www.scientific.net/kem.419-420.557 2010 Trans Tech Publications, Switzerland Utilizing Restricted Direction

More information

Research Article Vulnerability Analysis of Interdependent Scale-Free Networks with Complex Coupling

Research Article Vulnerability Analysis of Interdependent Scale-Free Networks with Complex Coupling Hindawi Electrical and Computer Engineering Volume 2017, Article ID 9080252, 5 pages https://doi.org/10.1155/2017/9080252 Research Article Vulnerability Analysis of Interdependent Scale-Free Networks with

More information

A Balancing Algorithm in Wireless Sensor Network Based on the Assistance of Approaching Nodes

A Balancing Algorithm in Wireless Sensor Network Based on the Assistance of Approaching Nodes Sensors & Transducers 2013 by IFSA http://www.sensorsportal.com A Balancing Algorithm in Wireless Sensor Network Based on the Assistance of Approaching Nodes 1,* Chengpei Tang, 1 Jiao Yin, 1 Yu Dong 1

More information

Research on Multi-sensor Image Matching Algorithm Based on Improved Line Segments Feature

Research on Multi-sensor Image Matching Algorithm Based on Improved Line Segments Feature ITM Web of Conferences, 0500 (07) DOI: 0.05/ itmconf/070500 IST07 Research on Multi-sensor Image Matching Algorithm Based on Improved Line Segments Feature Hui YUAN,a, Ying-Guang HAO and Jun-Min LIU Dalian

More information

Centrality Measures to Identify Traffic Congestion on Road Networks: A Case Study of Sri Lanka

Centrality Measures to Identify Traffic Congestion on Road Networks: A Case Study of Sri Lanka IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 2319-765X. Volume 13, Issue 2 Ver. I (Mar. - Apr. 2017), PP 13-19 www.iosrjournals.org Centrality Measures to Identify Traffic Congestion

More information

Onset of traffic congestion in complex networks

Onset of traffic congestion in complex networks Onset of traffic congestion in complex networks Liang Zhao, 1,2 Ying-Cheng Lai, 1,3 Kwangho Park, 1 and Nong Ye 4 1 Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287,

More information

γ : constant Goett 2 P(k) = k γ k : degree

γ : constant Goett 2 P(k) = k γ k : degree Goett 1 Jeffrey Goett Final Research Paper, Fall 2003 Professor Madey 19 December 2003 Abstract: Recent observations by physicists have lead to new theories about the mechanisms controlling the growth

More information

The Application of CAN Bus in Intelligent Substation Automation System Yuehua HUANG 1, a, Ruiyong LIU 2, b, Peipei YANG 3, C, Dongxu XIANG 4,D

The Application of CAN Bus in Intelligent Substation Automation System Yuehua HUANG 1, a, Ruiyong LIU 2, b, Peipei YANG 3, C, Dongxu XIANG 4,D International Power, Electronics and Materials Engineering Conference (IPEMEC 2015) The Application of CAN Bus in Intelligent Substation Automation System Yuehua HUANG 1, a, Ruiyong LIU 2, b, Peipei YANG

More information

The missing links in the BGP-based AS connectivity maps

The missing links in the BGP-based AS connectivity maps The missing links in the BGP-based AS connectivity maps Zhou, S; Mondragon, RJ http://arxiv.org/abs/cs/0303028 For additional information about this publication click this link. http://qmro.qmul.ac.uk/xmlui/handle/123456789/13070

More information

A new improved ant colony algorithm with levy mutation 1

A new improved ant colony algorithm with levy mutation 1 Acta Technica 62, No. 3B/2017, 27 34 c 2017 Institute of Thermomechanics CAS, v.v.i. A new improved ant colony algorithm with levy mutation 1 Zhang Zhixin 2, Hu Deji 2, Jiang Shuhao 2, 3, Gao Linhua 2,

More information

An Adaptive Threshold LBP Algorithm for Face Recognition

An Adaptive Threshold LBP Algorithm for Face Recognition An Adaptive Threshold LBP Algorithm for Face Recognition Xiaoping Jiang 1, Chuyu Guo 1,*, Hua Zhang 1, and Chenghua Li 1 1 College of Electronics and Information Engineering, Hubei Key Laboratory of Intelligent

More information

Consensus of Multi-Agent Systems with Prestissimo Scale-Free Networks

Consensus of Multi-Agent Systems with Prestissimo Scale-Free Networks Commun. Theor. Phys. (Beijing, China) 53 (2010) pp. 787 792 c Chinese Physical Society and IOP Publishing Ltd Vol. 53, No. 4, April 15, 2010 Consensus of Multi-Agent Systems with Prestissimo Scale-Free

More information