1. Definition In the context of Markov chains and stochastic processes , the index of 2 states refers to a classification or property of a pair of states within a finite Markov chain. More specifically, it relates to the periodicity and communicability between two states.
[ d_ij = \gcd n \geq 1 : P^n_ij > 0 = 2 ] index of 2 states
[ A \to B,\quad B \to A,\quad B \to C,\quad C \to B ] \quad B \to A