A sufficient condition for classified networks to possess complex network features

Xianmin Geng; Shengli Zhou; Jiashan Tang; Cong Yang

doi:10.3934/nhm.2012.7.59

Article Contents

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

This issue Previous Article Differential equation approximations of stochastic network processes: An operator semigroup approach Next Article Robot's finger and expansions in non-integer bases

A sufficient condition for classified networks to possess complex network features

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

Received: February 28, 2011

Revised: November 30, 2011

Published: February 2012

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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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Mathematics Subject Classification: Primary: 60D05, 90B15; Secondary: 60J20.

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