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
In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the model...In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively.展开更多
With the rapid development of big data, the scale of realistic networks is increasing continually. In order to reduce the network scale, some coarse-graining methods are proposed to transform large-scale networks into...With the rapid development of big data, the scale of realistic networks is increasing continually. In order to reduce the network scale, some coarse-graining methods are proposed to transform large-scale networks into mesoscale networks. In this paper, a new coarse-graining method based on hierarchical clustering (HCCG) on complex networks is proposed. The network nodes are grouped by using the hierarchical clustering method, then updating the weights of edges between clusters extract the coarse-grained networks. A large number of simulation experiments on several typical complex networks show that the HCCG method can effectively reduce the network scale, meanwhile maintaining the synchronizability of the original network well. Furthermore, this method is more suitable for these networks with obvious clustering structure, and we can choose freely the size of the coarse-grained networks in the proposed method.展开更多
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
In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the a...In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.展开更多
This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced drivi...This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving （DPAD） is introduced to reveal the dynamic structures in the networks supporting osciUations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center （say node A） and its driver （say node B） of a target wave can be used as a label, （A, B）, of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.展开更多
This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge＇s weights distribute uniformly but at random between them. It can describe the steady ...This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge＇s weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes＇ functions effectively. In order to detect the community structure efficiently, a threshold coefficient t~ to evaluate the equivalence of edges＇ weights and a new weighted modularity based on the weight＇s similarity are proposed. Then, constructing the weighted matrix and using the agglomerative mechanism, it presents a weight＇s agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes, the algorithm can detect the community structure in time O（n2 log~）. Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of t~ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.展开更多
A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a probl...A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a problem that has never been resolved before, for the Green＇s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.展开更多
In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of e...In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of economic consideration, in the evolutionary bus transport network model in P-space proposed by Chen et al （2007）. The degree distribution functions are derived by using the mean-field method and the master equation method, separately. The relationship between the new stop ratio of a route, λ, and the error in exponential of degree distribution function from the mean-field method is developed as ASlope= λ/（1 -λ） ＋ ln（1-λ）. Finally, the bus transport networks of Hangzhou and Nanjing are simulated by using this model, and the results show that some characteristic index values of the simulated networks are closer to the empirical data than those from Chen＇s model.展开更多
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.
文摘In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively.
文摘With the rapid development of big data, the scale of realistic networks is increasing continually. In order to reduce the network scale, some coarse-graining methods are proposed to transform large-scale networks into mesoscale networks. In this paper, a new coarse-graining method based on hierarchical clustering (HCCG) on complex networks is proposed. The network nodes are grouped by using the hierarchical clustering method, then updating the weights of edges between clusters extract the coarse-grained networks. A large number of simulation experiments on several typical complex networks show that the HCCG method can effectively reduce the network scale, meanwhile maintaining the synchronizability of the original network well. Furthermore, this method is more suitable for these networks with obvious clustering structure, and we can choose freely the size of the coarse-grained networks in the proposed method.
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.
文摘In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174034,11135001,11205041,and 11305112)the Natural ScienceFoundation of Jiangsu Province,China(Grant No.BK20130282)
文摘This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving （DPAD） is introduced to reveal the dynamic structures in the networks supporting osciUations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center （say node A） and its driver （say node B） of a target wave can be used as a label, （A, B）, of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.
基金supported by the Fundamental Research Funds for the Central Universities (Grant Nos. KYZ200916,KYZ200919 and KYZ201005)the Youth Sci-Tech Innovation Fund,Nanjing Agricultural University (Grant No. KJ2010024)
文摘This paper proposes the new definition of the community structure of the weighted networks that groups of nodes in which the edge＇s weights distribute uniformly but at random between them. It can describe the steady connections between nodes or some similarity between nodes＇ functions effectively. In order to detect the community structure efficiently, a threshold coefficient t~ to evaluate the equivalence of edges＇ weights and a new weighted modularity based on the weight＇s similarity are proposed. Then, constructing the weighted matrix and using the agglomerative mechanism, it presents a weight＇s agglomerative method based on optimizing the modularity to detect communities. For a network with n nodes, the algorithm can detect the community structure in time O（n2 log~）. Simulations on networks show that the algorithm has higher accuracy and precision than the existing techniques. Furthermore, with the change of t~ the algorithm discovers a special hierarchical organization which can describe the various steady connections between nodes in groups.
基金Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University,China(Grant No.15ZY16)
文摘A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a problem that has never been resolved before, for the Green＇s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.
基金supported by the National Natural Science Foundation of China (Grant No 70571033)the State Key Development Program for Basic Research of China (Grant No 2006CB705500)
文摘In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of economic consideration, in the evolutionary bus transport network model in P-space proposed by Chen et al （2007）. The degree distribution functions are derived by using the mean-field method and the master equation method, separately. The relationship between the new stop ratio of a route, λ, and the error in exponential of degree distribution function from the mean-field method is developed as ASlope= λ/（1 -λ） ＋ ln（1-λ）. Finally, the bus transport networks of Hangzhou and Nanjing are simulated by using this model, and the results show that some characteristic index values of the simulated networks are closer to the empirical data than those from Chen＇s model.
