  We study the diffusive transport of Markovian random walks on arbitrary
networks with stochastic resetting to multiple nodes. We deduce analytical
expressions for the stationary occupation probability and for the mean and
global first passage times. This general approach allows us to characterize the
effect of resetting on the capacity of random walk strategies to reach a
particular target or to explore the network. Our formalism holds for ergodic
random walks and can be implemented from the spectral properties of the random
walk without resetting, providing a tool to analyze the efficiency of search
strategies with resetting to multiple nodes. We apply the methods developed
here to the dynamics with two reset nodes and derive analytical results for
normal random walks and L\'evy flights on rings. We also explore the effect of
resetting to multiple nodes on a comb graph, L\'evy flights that visit specific
locations in a continuous space, and the Google random walk strategy on regular
networks.
