A sufficient condition for classified networks to possess complex network features

Xianmin Geng; Shengli Zhou; Jiashan Tang; Cong Yang; Xianmin Geng; Shengli Zhou; Jiashan Tang; Cong Yang

doi:10.3934/nhm.2012.7.59

Networks and Heterogeneous Media

2012, Volume 7, Issue 1: 59-69. doi: 10.3934/nhm.2012.7.59

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A sufficient condition for classified networks to possess complex network features

Xianmin Geng ^{1
,},
Shengli Zhou ^{1
,},
Jiashan Tang ^{2
,},
Cong Yang ^{1
,}

1.
College of Science, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016
2.
College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210046

Received: 01 March 2011 Revised: 01 December 2011
Primary: 60D05, 90B15; Secondary: 60J20.

We investigate network features for complex networks. A sufficient condition for the limiting random variable to possess the scale free property and the high clustering property is given. The uniqueness and existence of the limit of a sequence of degree distributions for the process is proved. The limiting degree distribution and a lower bound of the limiting clustering coefficient of the graph-valued Markov process are obtained as well.
- Scale free network,
- Clustering coefficient,
- Graph-valued stochastic process,
- Markovian process
Citation: Xianmin Geng, Shengli Zhou, Jiashan Tang, Cong Yang. A sufficient condition for classified networks to possess complex network features[J]. Networks and Heterogeneous Media, 2012, 7(1): 59-69. doi: 10.3934/nhm.2012.7.59

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Abstract

We investigate network features for complex networks. A sufficient condition for the limiting random variable to possess the scale free property and the high clustering property is given. The uniqueness and existence of the limit of a sequence of degree distributions for the process is proved. The limiting degree distribution and a lower bound of the limiting clustering coefficient of the graph-valued Markov process are obtained as well.

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