Hitting times for second-order random walks

A second-order random walk on a graph or network is where transition probabilities depend not only the present node but also previous one. notable example non-backtracking walk, walker allowed to revisit in one step. Second-order walks can model physical diffusion phenomena more realistic way than traditional and have been very successfully used various mining machine learning settings. However, numerous questions are still open for this type of stochastic processes. In work, we extend well-known results concerning mean hitting return times standard case. particular, provide simple formulas that allow us compute these numbers by solving suitable systems linear equations. Moreover, introducing ‘pullback’ first-order process versions renowned Kac’s Random Target Lemmas.