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THE ASYMPTOTIC DEGREE DISTRIBUTIONS OF RANDOM FAST GROWTH MODELS FOR TREELIKE NETWORKS

Published online by Cambridge University Press:  03 January 2017

Qunqiang Feng  and
Zhishui Hu
Qunqiang Feng
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China E-mail: fengqq@ustc.edu.cn; huzs@ustc.edu.cn
Zhishui Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China E-mail: fengqq@ustc.edu.cn; huzs@ustc.edu.cn
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Abstract

We propose two random network models for complex networks, which are treelike and always grow very fast. One is the uniform model and the other is the preferential attachment model, and both of them depends on a parameter 0<p<1. We first briefly discuss the network sizes, each of which can be corresponding to a supercritical branching process. And then we mainly study the degree distributions of both models. The asymptotic degree distribution of the first one with any parameter 0<p<1 is a geometric distribution with parameter 1/2, whereas that of the second one, which depends on p, can be uniquely determined by a functional equation of its probability generating function.

Keywords

complex networksdegree distributionfast growthpreferential attachmentrandom trees
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 2 , April 2017 , pp. 180 - 195
Copyright
Copyright © Cambridge University Press 2017 

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