PageRank of Gluing Networks and Corresponding Markov Chains

This paper studies Google’s PageRank algorithm. By an innovative application of the method of gluing Markov chains, we study the properties of Markov chains and extend their applicability by accounting for the damping factor and the personalization vector. Many properties of Markov chains related to spectrums and eigenvectors of the transition matrix, including the stationary distribution, periodicity, and persistent and transient states, will be investigated as well as part of the gluing process. Using the gluing formula, it is possible to decompose a large network into some sub-networks, compute their PageRank separably and glue them together. The computational workload can be reduced.