Biased random walks on networks with stochastic resetting

This study explores biased random walk dynamics with stochastic resetting on general networks. We show that the combination of biased random walks and stochastic resetting makes significant contributions by analyzing the search efficiency. We derive two analytical expressions for the stationary distribution and the mean first passage time, which are related to the spectral representation of the probability transition matrix of a biased random walk without resetting. These expressions can be used to determine the capacity of a random walker to reach the specific target and probe a finite network. We apply the analytical results to two types of networks, pseudofractal scale-free webs and T-fractals, which are constructed through an iterative process. We also extend a strategy to explore other complex structure networks or larger networks by leveraging the spectral properties.