In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in comp...In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.展开更多
Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolvi...Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.展开更多
The identification of the influential nodes in a network is of great significance for understanding the features of the network and controlling the complexity of networks in society and in biology. In this paper, we ...The identification of the influential nodes in a network is of great significance for understanding the features of the network and controlling the complexity of networks in society and in biology. In this paper, we propose a novel centrality measure for a node by considering the importance of edges and compare the performance of this method with existing seven topological-based ranking methods on the Susceptible-Infected-Recovered （SIR） model. The simulation results for four different types of real networks show that the proposed method is robust and exhibits excellent performance in identifying the most influential nodes when spreading starting from both single origin and multipleorigins simultaneously.展开更多
Identifying influential nodes in complex networks is still an open issue. In this paper, a new comprehensive centrality mea- sure is proposed based on the Dempster-Shafer evidence theory. The existing measures of degr...Identifying influential nodes in complex networks is still an open issue. In this paper, a new comprehensive centrality mea- sure is proposed based on the Dempster-Shafer evidence theory. The existing measures of degree centrality, betweenness centra- lity and closeness centrality are taken into consideration in the proposed method. Numerical examples are used to illustrate the effectiveness of the proposed method.展开更多
Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well a...Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm（DOCBVA）, an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.展开更多
A tiny fraction of influential individuals play a critical role in the dynamics on complex systems. Identifying the influential nodes in complex networks has theoretical and practical significance. Considering the unc...A tiny fraction of influential individuals play a critical role in the dynamics on complex systems. Identifying the influential nodes in complex networks has theoretical and practical significance. Considering the uncertainties of network scale and topology, and the timeliness of dynamic behaviors in real networks, we propose a rapid identifying method（RIM）to find the fraction of high-influential nodes. Instead of ranking all nodes, our method only aims at ranking a small number of nodes in network. We set the high-influential nodes as initial spreaders, and evaluate the performance of RIM by the susceptible-infected-recovered（SIR） model. The simulations show that in different networks, RIM performs well on rapid identifying high-influential nodes, which is verified by typical ranking methods, such as degree, closeness, betweenness,and eigenvector centrality methods.展开更多
Identifying influential nodes in complex networks is of both theoretical and practical importance. Existing methods identify influential nodes based on their positions in the network and assume that the nodes are homo...Identifying influential nodes in complex networks is of both theoretical and practical importance. Existing methods identify influential nodes based on their positions in the network and assume that the nodes are homogeneous. However, node heterogeneity （i.e., different attributes such as interest, energy, age, and so on ） ubiquitously exists and needs to be taken into consideration. In this paper, we conduct an investigation into node attributes and propose a graph signal pro- cessing based centrality （GSPC） method to identify influential nodes considering both the node attributes and the network topology. We first evaluate our GSPC method using two real-world datasets. The results show that our GSPC method effectively identifies influential nodes, which correspond well with the underlying ground truth. This is compatible to the previous eigenvector centrality and principal component centrality methods under circumstances where the nodes are homogeneous. In addition, spreading analysis shows that the GSPC method has a positive effect on the spreading dynamics.展开更多
Coarse graining of complex networks is an important method to study large-scale complex networks, and is also in the focus of network science today. This paper tries to develop a new coarse-graining method for complex...Coarse graining of complex networks is an important method to study large-scale complex networks, and is also in the focus of network science today. This paper tries to develop a new coarse-graining method for complex networks, which is based on the node similarity index. From the information structure of the network node similarity, the coarse-grained network is extracted by defining the local similarity and the global similarity index of nodes. A large number of simulation experiments show that the proposed method can effectively reduce the size of the network, while maintaining some statistical properties of the original network to some extent. Moreover, the proposed method has low computational complexity and allows people to freely choose the size of the reduced networks.展开更多
On the basis of complex network theory, the issues of key nodes in Wireless Sensor Networks (WSN) are discussed. A model expression of sub-network fault in WSN is given at first; subsequently, the concepts of average ...On the basis of complex network theory, the issues of key nodes in Wireless Sensor Networks (WSN) are discussed. A model expression of sub-network fault in WSN is given at first; subsequently, the concepts of average path length and clustering coefficient are introduced. Based on the two concepts, a novel attribute description of key nodes related to sub-networks is proposed. Moreover, in terms of node deployment density and transmission range, the concept of single-point key nodes and generalized key nodes of WSN are defined, and their decision theorems are investigated.展开更多
In this paper, we investigate the impulsive synchronization between two coupled complex networks with time- delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive contr...In this paper, we investigate the impulsive synchronization between two coupled complex networks with time- delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat＇s lemma, the global asymptotic impulsive synchronization of the drive-response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.展开更多
In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitative...In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described. Results of node degrees for the Northern Hemisphere （NH） mid-high latitude （30° N-90°N） circulation system （NHS） networks with and without the Arctic Oscillations （AO）, the North Atlantic Oscillations （NAO） and the Pacific-North American pattern （PNA） demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks, thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS. The impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important. The PNA is a relatively independent teleconnection, and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system （TRS）. As to the Southern Hemisphere mid-high latitude （30°S-90°S） circulation system （SHS）, the impact of the Antarctic Arctic Oscillations （AAO） on the structural stability of the system is most important. In addition, there might be a stable correlation dipole （AACD） in the SHS, which also has important influence on the structure of the SHS networks.展开更多
In order to study the nodes importance and its evolution process of the railway network of SREB (Silk Road Economic Belt), we construct the network (RNSREB) based on Graph Theory, which focuses on the time intervals a...In order to study the nodes importance and its evolution process of the railway network of SREB (Silk Road Economic Belt), we construct the network (RNSREB) based on Graph Theory, which focuses on the time intervals according to actually railway network, railway project under construction and the national railway network of medium-and long-term plan. The algorithms for vital nodes evaluation are analyzed, the evaluation method on nodes importance of RNSREB is proposed, the quantized values of each node are calculated with Pajek, and TOP20 core nodes of the network with different coefficients and time intervals are determined respectively. Then the evolution process of TOP20 critical nodes with 4 periods is contrasted and analyzed. It is indicated that some vital nodes newly discovered (Geermu, Maduo, Ruoqiang) should be concerned.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61573017)the Natural Science Foundation of Shaanxi Province,China(Grant No.2016JQ6062)
文摘In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence（IS） to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.
基金supported by the National Natural Science Foundation of China(615730176140149961174162)
文摘Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.
基金Supported by the Research Foundation of Hubei Province Department of Education(Q20151505)the East China Jiaotong University Doctor Scientific Research Start Fund Project(26441021)
文摘The identification of the influential nodes in a network is of great significance for understanding the features of the network and controlling the complexity of networks in society and in biology. In this paper, we propose a novel centrality measure for a node by considering the importance of edges and compare the performance of this method with existing seven topological-based ranking methods on the Susceptible-Infected-Recovered （SIR） model. The simulation results for four different types of real networks show that the proposed method is robust and exhibits excellent performance in identifying the most influential nodes when spreading starting from both single origin and multipleorigins simultaneously.
基金supported by the National Natural Science Foundation of China(61174022)the National High Technology Research and Development Program of China(863 Program)(2013AA013801)+2 种基金the Open Funding Project of State Key Laboratory of Virtual Reality Technology and Systems,Beihang University(BUAA-VR-14KF-02)the General Research Program of the Science Supported by Sichuan Provincial Department of Education(14ZB0322)the Fundamental Research Funds for the Central Universities(XDJK2014D008)
文摘Identifying influential nodes in complex networks is still an open issue. In this paper, a new comprehensive centrality mea- sure is proposed based on the Dempster-Shafer evidence theory. The existing measures of degree centrality, betweenness centra- lity and closeness centrality are taken into consideration in the proposed method. Numerical examples are used to illustrate the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61672124,61370145,61173183,and 61503375)the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund,China(Grant No.MMJJ20170203)
文摘Detection of community structures in the complex networks is significant to understand the network structures and analyze the network properties. However, it is still a problem on how to select initial seeds as well as to determine the number of communities. In this paper, we proposed the detecting overlapping communities based on vital nodes algorithm（DOCBVA）, an algorithm based on vital nodes and initial seeds to detect overlapping communities. First, through some screening method, we find the vital nodes and then the seed communities through the pretreatment of vital nodes. This process differs from most existing methods, and the speed is faster. Then the seeds will be extended. We also adopt a new parameter of attribution degree to extend the seeds and find the overlapping communities. Finally, the remaining nodes that have not been processed in the first two steps will be reprocessed. The number of communities is likely to change until the end of algorithm. The experimental results using some real-world network data and artificial network data are satisfactory and can prove the superiority of the DOCBVA algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374180 and 61373136)the Ministry of Education Research in the Humanities and Social Sciences Planning Fund Project,China(Grant No.12YJAZH120)the Six Projects Sponsoring Talent Summits of Jiangsu Province,China(Grant No.RLD201212)
文摘A tiny fraction of influential individuals play a critical role in the dynamics on complex systems. Identifying the influential nodes in complex networks has theoretical and practical significance. Considering the uncertainties of network scale and topology, and the timeliness of dynamic behaviors in real networks, we propose a rapid identifying method（RIM）to find the fraction of high-influential nodes. Instead of ranking all nodes, our method only aims at ranking a small number of nodes in network. We set the high-influential nodes as initial spreaders, and evaluate the performance of RIM by the susceptible-infected-recovered（SIR） model. The simulations show that in different networks, RIM performs well on rapid identifying high-influential nodes, which is verified by typical ranking methods, such as degree, closeness, betweenness,and eigenvector centrality methods.
基金supported by the National Natural Science Foundation of China(Grant No.61231010)the Fundamental Research Funds for the Central Universities,China(Grant No.HUST No.2012QN076)
文摘Identifying influential nodes in complex networks is of both theoretical and practical importance. Existing methods identify influential nodes based on their positions in the network and assume that the nodes are homogeneous. However, node heterogeneity （i.e., different attributes such as interest, energy, age, and so on ） ubiquitously exists and needs to be taken into consideration. In this paper, we conduct an investigation into node attributes and propose a graph signal pro- cessing based centrality （GSPC） method to identify influential nodes considering both the node attributes and the network topology. We first evaluate our GSPC method using two real-world datasets. The results show that our GSPC method effectively identifies influential nodes, which correspond well with the underlying ground truth. This is compatible to the previous eigenvector centrality and principal component centrality methods under circumstances where the nodes are homogeneous. In addition, spreading analysis shows that the GSPC method has a positive effect on the spreading dynamics.
文摘Coarse graining of complex networks is an important method to study large-scale complex networks, and is also in the focus of network science today. This paper tries to develop a new coarse-graining method for complex networks, which is based on the node similarity index. From the information structure of the network node similarity, the coarse-grained network is extracted by defining the local similarity and the global similarity index of nodes. A large number of simulation experiments show that the proposed method can effectively reduce the size of the network, while maintaining some statistical properties of the original network to some extent. Moreover, the proposed method has low computational complexity and allows people to freely choose the size of the reduced networks.
基金Supported by the National High Technology Research and Development Program of China(No.2008AA01A201)the National Natural Science Foundation of China(No.60503015)
文摘On the basis of complex network theory, the issues of key nodes in Wireless Sensor Networks (WSN) are discussed. A model expression of sub-network fault in WSN is given at first; subsequently, the concepts of average path length and clustering coefficient are introduced. Based on the two concepts, a novel attribute description of key nodes related to sub-networks is proposed. Moreover, in terms of node deployment density and transmission range, the concept of single-point key nodes and generalized key nodes of WSN are defined, and their decision theorems are investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No.70871056)the Six Talents Peak Foundation of Jiangsu Province,China
文摘In this paper, we investigate the impulsive synchronization between two coupled complex networks with time- delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat＇s lemma, the global asymptotic impulsive synchronization of the drive-response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.40930952 and 40705031)the Special Scientific Research Project for Public Interest,China (Grant Nos.GYHY201006021 and GYHY201106016)the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No.2007BAC29B01)
文摘In terms of the characteristic topology parameters of climate complex networks, the spatial connection structural complexity of the circulation system and the influence of four teleconnection patterns are quantitatively described. Results of node degrees for the Northern Hemisphere （NH） mid-high latitude （30° N-90°N） circulation system （NHS） networks with and without the Arctic Oscillations （AO）, the North Atlantic Oscillations （NAO） and the Pacific-North American pattern （PNA） demonstrate that the teleconnections greatly shorten the mean shortest path length of the networks, thus being advantageous to the rapid transfer of local fluctuation information over the network and to the stability of the NHS. The impact of the AO on the NHS connection structure is most important and the impact of the NAO is the next important. The PNA is a relatively independent teleconnection, and its role in the NHS is mainly manifested in the connection between the NHS and the tropical circulation system （TRS）. As to the Southern Hemisphere mid-high latitude （30°S-90°S） circulation system （SHS）, the impact of the Antarctic Arctic Oscillations （AAO） on the structural stability of the system is most important. In addition, there might be a stable correlation dipole （AACD） in the SHS, which also has important influence on the structure of the SHS networks.
文摘In order to study the nodes importance and its evolution process of the railway network of SREB (Silk Road Economic Belt), we construct the network (RNSREB) based on Graph Theory, which focuses on the time intervals according to actually railway network, railway project under construction and the national railway network of medium-and long-term plan. The algorithms for vital nodes evaluation are analyzed, the evaluation method on nodes importance of RNSREB is proposed, the quantized values of each node are calculated with Pajek, and TOP20 core nodes of the network with different coefficients and time intervals are determined respectively. Then the evolution process of TOP20 critical nodes with 4 periods is contrasted and analyzed. It is indicated that some vital nodes newly discovered (Geermu, Maduo, Ruoqiang) should be concerned.
