On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of...On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of alot of cliques,which intensively connect and overlap with each other.We study the network properties,which includethe degree distribution,multiple edges' overlapping time distribution,distribution of the overlap size between any twooverlapping cliques,distribution of the number of cliques that a node belongs to.Naturally,the cliques also constitute anetwork,with the overlapping nodes being their multiple links.We also research its network properties such as degreedistribution,clustering,average path length,and so on.We propose that a BTN has the properties of random cliqueincrement and random overlapping clique,at the same time,a BTN is a small-world network with highly clique-clusteredand highly clique-overlapped.Finally,we introduce a BTN evolution model,whose simulation results agree well withthe statistical laws that emerge in real BTNs.展开更多
A novel scale-flee network model based on clique （complete subgraph of random size） growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving ...A novel scale-flee network model based on clique （complete subgraph of random size） growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P（d） is 2m^2m1^-3（d-m1 ＋ 1）^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P（k） is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.展开更多
We developed a computational framework to identify common gene association sub-network. This framework combines graphical lasso model, graph product and a replicator equation based clique solver. We applied this metho...We developed a computational framework to identify common gene association sub-network. This framework combines graphical lasso model, graph product and a replicator equation based clique solver. We applied this method to find common stress responsive sub-networks from two related Deinococcus-Thermus bacterial species.展开更多
A novel weighted evolving network model based on the clique overlapping growth was proposed.The model shows different network characteristics under two different selection mechanisms that are preferential selection an...A novel weighted evolving network model based on the clique overlapping growth was proposed.The model shows different network characteristics under two different selection mechanisms that are preferential selection and random selection.On the basis of mean-field theory,this model under the two different selection mechanisms was analyzed.The analytic equations of distributions of the number of cliques that a vertex joins and the vertex strength of the model were given.It is proved that both distributions follow the scale-free power-law distribution in preferential selection mechanism and the exponential distribution in random selection mechanism,respectively.The analytic expressions of exponents of corresponding distributions were obtained.The agreement between the simulations and analytical results indicates the validity of the theoretical analysis.Finally,three real transport bus networks(BTNs) of Beijing,Shanghai and Hangzhou in China were studied.By analyzing their network properties,it is discovered that these real BTNs belong to a kind of weighted evolving network model with clique overlapping growth and random selection mechanism that was proposed in this context.展开更多
We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique （maximal complete sub-graph） at. each time step. And the cliques in the network overlap with each othe...We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique （maximal complete sub-graph） at. each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges＇ weight and vertices＇ strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights＇ enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices＇ strength and the distribution o~ edges＇ weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices＇ strength and edges＇ weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.展开更多
The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which ...The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by sev- eral examples.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.60504027 and 60874080the Postdoctor Science Foundation of China under Grant No.20060401037
文摘On the basis of investigating the statistical data of bus transport networks of three big cities in China,wepropose that each bus route is a clique(maximal complete subgraph)and a bus transport network(BTN)consists of alot of cliques,which intensively connect and overlap with each other.We study the network properties,which includethe degree distribution,multiple edges' overlapping time distribution,distribution of the overlap size between any twooverlapping cliques,distribution of the number of cliques that a node belongs to.Naturally,the cliques also constitute anetwork,with the overlapping nodes being their multiple links.We also research its network properties such as degreedistribution,clustering,average path length,and so on.We propose that a BTN has the properties of random cliqueincrement and random overlapping clique,at the same time,a BTN is a small-world network with highly clique-clusteredand highly clique-overlapped.Finally,we introduce a BTN evolution model,whose simulation results agree well withthe statistical laws that emerge in real BTNs.
基金Projects(60504027,60573123) supported by the National Natural Science Foundation of ChinaProject(20060401037) supported by the National Postdoctor Science Foundation of ChinaProject(X106866) supported by the Natural Science Foundation of Zhejiang Province,China
文摘A novel scale-flee network model based on clique （complete subgraph of random size） growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P（d） is 2m^2m1^-3（d-m1 ＋ 1）^-3, where m and m1 denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P（k） is 2m^2Ek^-3, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-flee power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.
文摘We developed a computational framework to identify common gene association sub-network. This framework combines graphical lasso model, graph product and a replicator equation based clique solver. We applied this method to find common stress responsive sub-networks from two related Deinococcus-Thermus bacterial species.
基金Projects(60874080,60504027) supported by the National Natural Science Foundation of ChinaProject(20060401037) supported by the National Postdoctor Science Foundation of China
文摘A novel weighted evolving network model based on the clique overlapping growth was proposed.The model shows different network characteristics under two different selection mechanisms that are preferential selection and random selection.On the basis of mean-field theory,this model under the two different selection mechanisms was analyzed.The analytic equations of distributions of the number of cliques that a vertex joins and the vertex strength of the model were given.It is proved that both distributions follow the scale-free power-law distribution in preferential selection mechanism and the exponential distribution in random selection mechanism,respectively.The analytic expressions of exponents of corresponding distributions were obtained.The agreement between the simulations and analytical results indicates the validity of the theoretical analysis.Finally,three real transport bus networks(BTNs) of Beijing,Shanghai and Hangzhou in China were studied.By analyzing their network properties,it is discovered that these real BTNs belong to a kind of weighted evolving network model with clique overlapping growth and random selection mechanism that was proposed in this context.
基金Supported by National Natural Science Foundation of China under Grant Nos. 60504027 and 60874080the Open Project of State Key Lab of Industrial Control Technology under Grant No. ICT1107
文摘We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique （maximal complete sub-graph） at. each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges＇ weight and vertices＇ strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights＇ enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices＇ strength and the distribution o~ edges＇ weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices＇ strength and edges＇ weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.
文摘The maximum clique or maximum independent set of graph is a classical problem in graph theory. Com- bined with Boolean algebra and integer programming, two integer programming models for maximum clique problem, which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by sev- eral examples.
