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Title: A vertex-number-evolving Markov chain of networks
Authors: Shi, D
Xua, H
Liu L 
Keywords: BA model
Convergence in probability
Initial attraction model
LCD model
Markov chain
Scale-free network
Vertex number with degree k
Issue Date: 2010
Publisher: Elsevier
Source: Physics procedia, 2010, v. 3, no. 5, p. 1757-1765 How to cite?
Journal: Physics procedia 
Abstract: We have introduced a vector Markov chain of the vertex number with degree k in network evolving process as a framework of theoretical analysis and proved the stability of the BA-1 model and the LCD-1 model. In this paper, we use the vertex-number-evolving Markov chain to prove rigorously the existence of the steady-state degree distribution P(k) for a special case of the initial attraction model allowing multiple edges. The application of our approach to the LCD-m model, the result shows that it is more simpler than Bollobás' method.
EISSN: 1875-3884
DOI: 10.1016/j.phpro.2010.07.016
Rights: © 2010 Published by Elsevier Ltd Open access under the CC BY-NC-ND license (
The following publication Shi, D., Xua, H., & Liu, L. (2010). A vertex-number-evolving Markov chain of networks. Physics procedia, 2010, 3(5), 1757-1765 is available at
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