Biased Random Search on Directed Networks with Stochastic Resetting

This study investigates biased random walks with stochastic resetting on directed networks. By employing the spectral decomposition of the transition probability matrix, we derive analytical expressions for the stationary distribution and mean first-passage time (MFPT), providing a quantitative framework for characterizing search efficiency in directed systems. Furthermore, we establish a general criterion for optimal resetting and derive sufficient conditions for its existence. The theoretical results are validated through extensive numerical simulations on three representative synthetic networks and three real-world directed networks, demonstrating the applicability of the proposed framework across diverse topologies. These findings provide a systematic understanding of how biased random walks combined with stochastic resetting can improve search efficiency under suitable structural conditions.