Reducing Kolmogorov's Reversibility Criterion Via a Basis for the Interaction Graph Kernel

In this work, we define the interaction graph for a continuous-time Markov chain to analyze its dynamic structure. Under certain assumptions, we demonstrate that verifying Kolmogorov’s reversibility criterion reduces to checking it for a cycle basis of the incidence matrix kernel associated with the interaction graph. This result provides an efficient tool for verifying reversibility in Markov continuous chains.