Higher-order random walks on complex networks

We investigate higher order random walks on complex networks for which the walker jumps among higher-order substructures. By using the binary normalization method, we obtain its stationary distribution analytically. Moreover, we derive the analytical expression for the mean first passage time of higher-order random walks. Remarkably, we find that in the same circumstance, more time is required for higher-order random walk search in comparison with random walks. Our work provides another random search navigation way on complex networks thoroughly deviating from random walks.