Partial cover time that is sublinear in the number of targets on complex networks: a universal law

Abstract We investigate random search processes on complex networks and for the first time derive an exact expression for the partial cover time that quantifies the time a walker needs to visit multiple targets. Based on that, we find some invariant metrics like the effects of source location and the scale exponent of the size effect, which are independent of the target number. Interestingly, we observe the slow, logarithmic increase of the global partial cover time with the target number across various real networks. This suggests that more unvisited targets could be easily found by spending only a little extra time. This finding has practical applications in a broad range of areas where random searches are used to model complex dynamical processes.