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 of mean first passage time of higher-order random walks. Remarkably, we find that in the same circumstance, more time are required for higher-order random walk search in comparsion with random walks. Our work provides another random search navigation way on complex networks throughly deviating from random walks.