With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential atta...With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential attachment is researched to solve an actual network CCN （Cooperative Communication Network）. Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution and average path length. The results of this paper are more significant for building CCN to programme the resource of communication.展开更多
This paper theoretically and empirically studies the degree and connectivity of the Internet＇s scale-free topology at an autonomous system （AS） level. The basic features of scale-free networks influence the normali...This paper theoretically and empirically studies the degree and connectivity of the Internet＇s scale-free topology at an autonomous system （AS） level. The basic features of scale-free networks influence the normalization constant of degree distribution p（k）. It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the kmin-degree （minimum degree） nodes and the kmax-degree （maximum degree） nodes, and the fraction of the degrees （or links） in the hands of the richer （top best-connected） nodes. It finds that the average degree is larger for a smaller power-law exponent A and a larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger λ and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller λ and kmax or larger kmin. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the kmin-degree nodes has power-law decay with the increase of kmin. The ratio of the kmax-degree nodes has a power-law decay with the increase of kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% （the 73/27 rule＇）. Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology.展开更多
We investigate correlations between neighbor degrees in the scale-free network. According to the empirical studies, it is known that the degree correlations exhibit nontrivial statistical behaviors. With using an anal...We investigate correlations between neighbor degrees in the scale-free network. According to the empirical studies, it is known that the degree correlations exhibit nontrivial statistical behaviors. With using an analytical approach, we show that the scale-freeness and one of statistical laws for degree correlations can be reproduced consistently in a unified framework. Our result would have its importance in understanding the mechanisms which generate the complex network.展开更多
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a correspond...In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.展开更多
In this paper, we propose a difference equation approach to the estimation of the degree distributions in growing networks after having analyzed the disadvantages of some existing approaches. This approach can avoid l...In this paper, we propose a difference equation approach to the estimation of the degree distributions in growing networks after having analyzed the disadvantages of some existing approaches. This approach can avoid logic conflicts caused by the continuum of discrete problems, and does not need the existence assumption of the stationary degree distribution in the network analysis. Using this approach, we obtain a degree distribution formula of the Poisson growth and preferential attachment network. It is rigorously shown that this network is scale-free based on the Poisson process theory and properties of F-distribution.展开更多
Monkey language models are defined for Chi-nese Phrase Networks, and scale-free features of Chinese Phrase Networks are uncovered. It is pointed out that the ratio of average degree to the total number of nodes ( k /N...Monkey language models are defined for Chi-nese Phrase Networks, and scale-free features of Chinese Phrase Networks are uncovered. It is pointed out that the ratio of average degree to the total number of nodes ( k /N ) is close to a constant. Simulation for the evolution of phrase networks indicates that one of the important reasons for power law distributions is the word selection frequency, which, when tuned aptly, can make the monkey language present similar statistic traits as that of natural languages. Power law tails emerge at large k, and the exponent is about 6. Comparison between monkey model and natural language shows that humans are able to use Chinese words resources in more effective and compact ways to express their inten-tions. All the results demonstrate an important fact that the least effort principle is the basis of Chinese Phrase Networks.展开更多
基金Project supported by the Natural Science Foundation of Beijing(Grant No.4152035)the National Natural Science Foundation of China(Grant No.61272507)
文摘With the requirements of users enhanced for wireless communication, the cooperative communication will become a development trend in future. In this paper, a model based on complex networks with both preferential attachment is researched to solve an actual network CCN （Cooperative Communication Network）. Firstly, the evolution of CCN is given by four steps with different probabilities. At the same time, the rate equations of nodes degree are presented to analyze the evolution of CCN. Secondly, the degree distribution is analyzed by calculating the rate equation and numerical simulation. Finally, the robustness of CCN is studied by numerical simulation with random attack and intentional attack to analyze the effects of degree distribution and average path length. The results of this paper are more significant for building CCN to programme the resource of communication.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60973129,60903058 and 60903168)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 200805331109)+1 种基金the China Postdoctoral Science Foundation (Grant No. 200902324)the Program for Excellent Talents in Hunan Normal University,China (Grant No. ET10902)
文摘This paper theoretically and empirically studies the degree and connectivity of the Internet＇s scale-free topology at an autonomous system （AS） level. The basic features of scale-free networks influence the normalization constant of degree distribution p（k）. It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the kmin-degree （minimum degree） nodes and the kmax-degree （maximum degree） nodes, and the fraction of the degrees （or links） in the hands of the richer （top best-connected） nodes. It finds that the average degree is larger for a smaller power-law exponent A and a larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger λ and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller λ and kmax or larger kmin. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the kmin-degree nodes has power-law decay with the increase of kmin. The ratio of the kmax-degree nodes has a power-law decay with the increase of kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% （the 73/27 rule＇）. Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology.
文摘We investigate correlations between neighbor degrees in the scale-free network. According to the empirical studies, it is known that the degree correlations exhibit nontrivial statistical behaviors. With using an analytical approach, we show that the scale-freeness and one of statistical laws for degree correlations can be reproduced consistently in a unified framework. Our result would have its importance in understanding the mechanisms which generate the complex network.
基金Supported by National Natural Science Foundation of China (Grant No. 10901164)Graduate Research Innovation Projects in Hunan Province (Grant No. CX2009B020)+2 种基金Graduate Degree Thesis Innovation Foundation of Central South University (Grant No. 2009ybfz11)supported by Natural Science Foundation of China (Grant Nos. 11071258, 90820302)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090162110058)
文摘In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.
基金supported by the National Natural Science Foundation of China (No. 70871082)the Foundation of Shanghai Leading Academic Discipline Project (No. S30504)
文摘In this paper, we propose a difference equation approach to the estimation of the degree distributions in growing networks after having analyzed the disadvantages of some existing approaches. This approach can avoid logic conflicts caused by the continuum of discrete problems, and does not need the existence assumption of the stationary degree distribution in the network analysis. Using this approach, we obtain a degree distribution formula of the Poisson growth and preferential attachment network. It is rigorously shown that this network is scale-free based on the Poisson process theory and properties of F-distribution.
文摘Monkey language models are defined for Chi-nese Phrase Networks, and scale-free features of Chinese Phrase Networks are uncovered. It is pointed out that the ratio of average degree to the total number of nodes ( k /N ) is close to a constant. Simulation for the evolution of phrase networks indicates that one of the important reasons for power law distributions is the word selection frequency, which, when tuned aptly, can make the monkey language present similar statistic traits as that of natural languages. Power law tails emerge at large k, and the exponent is about 6. Comparison between monkey model and natural language shows that humans are able to use Chinese words resources in more effective and compact ways to express their inten-tions. All the results demonstrate an important fact that the least effort principle is the basis of Chinese Phrase Networks.
