Calculating rate constants and committor probabilities for transition networks by graph transformation

A graph transformation procedure is described that enables waiting times, rate constants, and committor probabilities to be calculated within a single scheme for finite-state discrete-time Markov processes. The scheme is applicable to any transition network where the states, equilibrium occupation probabilities, and transition probabilities are specified. For networks involving many states or slow overall kinetics, the deterministic graph transformation approach is faster and more accurate than direct diagonalization of the transition matrix, kinetic Monte Carlo, or iterative procedures.