Random walks on complex networks under node-dependent stochastic resetting

In the present work, we study random walks on complex networks subject to stochastic resetting when the resetting probability is node-dependent. Using a renewal approach, we derive the exact expressions of the stationary occupation probabilities of the walker on each node and the mean first passage time between arbitrary two nodes. Finally, we demonstrate our theoretical results on three networks with two different resetting protocols, validated by numerical simulations as well. We find that under a delicate setting it is advantageous to optimize the efficiency of a global search on such networks by the node-dependent resetting probability.