Sensitivity Analysis Of Group Inverse In Markov Chains And Block Analysis Of Small World Phenomena

let P be the transition matrix of a discrete-time Markov chain.The group inverse(I-P)~# plays an important role in the analysis of the Markov chain.In this paper we analyzed the sensitivity of group inverse under the entrywise perturbation in P.The error bound shows that the sensitivity is independent of the condition of the Markov chain. We also did research on small world model based on block matrices and illustrated the existence of the small world phenomena.