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On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks

Published online by Cambridge University Press:  28 May 2015

Xutao Li ,
Wen Li ,
Michael K. Ng  and
Yunming Ye
Xutao Li*
Affiliation:
Department of Computer Science, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
Wen Li*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
Michael K. Ng*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Yunming Ye*
Affiliation:
Department of Computer Science, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
*
Corresponding author.Email address:xutaolee08@gmail.com
Corresponding author.Email address:liwen@scnu.edu.cn
Corresponding author.Email address:mng@math.hkbu.edu.hk
Corresponding author.Email address:yeyunming@hit.edu.cn
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Abstract

Node importance or centrality evaluation is an important methodology for network analysis. In this paper, we are interested in the study of objects appearing in several networks. Such common objects are important in network-network interactions via object-object interactions. The main contribution of this paper is to model multiple networks where there are some common objects in a multivariate Markov chain framework, and to develop a method for solving common and non-common objects’ stationary probability distributions in the networks. The stationary probability distributions can be used to evaluate the importance of common and non-common objects via network-network interactions. Our experimental results based on examples of co-authorship of researchers in different conferences and paper citations in different categories have shown that the proposed model can provide useful information for researcher-researcher interactions in networks of different conferences and for paper-paper interactions in networks of different categories.

Keywords

60J1091D3005C81transition probability multivariate Markov chainsstationary probability distributionirreduciblemultiple networks
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 3 , August 2012 , pp. 384 - 402
Copyright
Copyright © Global Science Press Limited 2012

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