A vertex-number-evolving Markov chain of networks

Dinghua SHI, Hong XU, Liming LIU*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)

1 Scopus Citations


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.

Original languageEnglish
Pages (from-to)1757-1765
Number of pages9
JournalPhysics Procedia
Issue number5
Publication statusPublished - Aug 2010
Externally publishedYes



  • BA model
  • Convergence in probability
  • Initial attraction model
  • LCD model
  • Markov chain
  • Scale-free network
  • Stability
  • Vertex number with degree k

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