Chin. Phys. Lett.  2009, Vol. 26 Issue (3): 038901    DOI: 10.1088/0256-307X/26/3/038901
CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
Stability of the BA Network: a New Approach to Rigorous Proof
XU Hong, SHI Ding-Hua
Department of Mathematics, Shanghai University, Shanghai 200444
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XU Hong, SHI Ding-Hua 2009 Chin. Phys. Lett. 26 038901
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Abstract We propose a new approach to rigorously prove the existence of the steady-state degree distribution for the BA network. The approach is based on a vector Markov chain of vertex numbers in the network evolving process. This framework provides a rigorous theoretical basis for the rate equation approach which has been widely applied to many problems in the field of complex networks, e.g., epidemic spreading and dynamic synchronization.
Keywords: 89.75.Hc      02.50.Ga      89.75.Da     
Received: 24 November 2008      Published: 19 February 2009
PACS:  89.75.Hc (Networks and genealogical trees)  
  02.50.Ga (Markov processes)  
  89.75.Da (Systems obeying scaling laws)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/3/038901       OR      https://cpl.iphy.ac.cn/Y2009/V26/I3/038901
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XU Hong
SHI Ding-Hua
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