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 - <p style="text-align: justify;">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&#39; 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.</p>