Abstract
There is a growing interest in the analysis of networks found in the World Wide Web and in social networks. A common feature of these networks is that the finite-state Markov chain modeling the influence relation between nodes typically has several (nearly) ergodic classes. This paper introduces a new decomposition algorithm for Markov chains that allows to split the graph of the Markov chain into subgraphs such that the connectivity of the chain—measured by the Kemeny constant—is maximally decreased. In other words, we show how the structure dormant in a nearly decomposable chain can be brought to light. We present applications to influence ranking in social networks, decomposition of a social network into subnetworks, and cluster analysis.
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