Volume 5, Issue 3
On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks

Xutao Li, Wen Li, Michael K. Ng & Yunming Ye

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 384-402.

Published online: 2012-05

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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

Transition probability, multivariate Markov chains, stationary probability distribution, irreducible, multiple networks.

  • AMS Subject Headings

60J10, 91D30, 05C81

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-384, author = {}, title = {On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {3}, pages = {384--402}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m1108}, url = {http://global-sci.org/intro/article_detail/nmtma/5943.html} }
TY - JOUR T1 - On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 384 EP - 402 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m1108 UR - https://global-sci.org/intro/article_detail/nmtma/5943.html KW - Transition probability, multivariate Markov chains, stationary probability distribution, irreducible, multiple networks. AB -

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.

Xutao Li, Wen Li, Michael K. Ng & Yunming Ye. (2020). On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks. Numerical Mathematics: Theory, Methods and Applications. 5 (3). 384-402. doi:10.4208/nmtma.2012.m1108
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