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

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 interac- tions 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 ob- jects' stationary probability distributions in the networks. The stationary probability distributions can be used to evaluate the importance of common and non-common ob- jects via network-network interactions. Our experimental results based on examples of co-authorship of researchers in different conferences and paper citations in differ- ent 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. AMS subject classifications: 60J10, 91D30, 05C81