Markov chain small-world model with asymmetry: A unified and multivariate perspective

An extended Markov chain small-world network model involving asymmetric transitions is further investigated here. Exact results on the maximum mean first passage time are established. These results also unify the special symmetric case, which was studied by Catral, Neumann, and Xu and Higham, respectively. In addition, they allow the model to be approached in a new, multivariate perspective, which is not feasible with existing asymptotic results. An interesting outcome from this study is that the small-world phenomenon on the model is largely enhanced while passing from the symmetric case to the asymmetric case. This is in accordance with some recent results obtained from numerical simulation on an extended Watts–Strogatz model.