In this paper, we propose an evolving random network. The model is a linear combination of preferential attachment model and uniform model. We show that scaling limit distribution of the number of leaves at time n is ...In this paper, we propose an evolving random network. The model is a linear combination of preferential attachment model and uniform model. We show that scaling limit distribution of the number of leaves at time n is approximated by nomal distribution and the proportional degree sequence obeys power law. The branching structure and maximum degree are also discussed in this paper.展开更多
Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of compl...Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.展开更多
基金The NSF (71271003) of Chinathe Programming Fund (12YJC630111, 12YJA790041) of the Humanities adn Social Sciences Research of the Ministry of Education of China+1 种基金the NSF (10040606Q03) of Anhui ProvinceKey University Science Research Project (KJ2013A044) of Anhui Province
文摘In this paper, we propose an evolving random network. The model is a linear combination of preferential attachment model and uniform model. We show that scaling limit distribution of the number of leaves at time n is approximated by nomal distribution and the proportional degree sequence obeys power law. The branching structure and maximum degree are also discussed in this paper.
基金Project supported by the Research Foundation from Ministry of Science and Technology, China （Grant Nos 2006AA02Z317,2004CB720103, 2003CB715901 and 2006AA02312）, the National High Technology Research and Development Program of China （Grant No 2006AA020805）, the National Natural Science Foundation of China （Grant Nos 30500107, 30670953 and 30670574）, the International Cooperation Project of Science and Technology Commission of Shanghai Municipality, China （Grant No 06RS07109）, and Grant from Science and Technology Commission of Shanghai Municipality, China （Grant Nos 04DZ19850, 06PJ14072 and 04DZ 14005）.Acknowledgement We thank Luis A. Nunes Amaral and Roger Guimerà for kindly providing us with the software Modul-w of computing the network modularity metric. Our gratitude must also be extended to John Doyle, Petter Holme and Lun Li for useful discussion and constructive comments.
文摘Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.
基金Supported by National Natural Science Foundation of China(10971137)National Key Basic Research(973)Program of China(2006CB805900)a grant from Science and Technology Commission of Shanghai Municipality(09XD1402500)
基金supported by NSFC(Grant NO.60872060)Shanghai Citylevel Finance Departmen- tal Budget Project(1138IA0005/1139IA0013)the Innovation Program of Shanghai Municipal Education Commission(11yz241)
