We consider the problem of identifying rumor sources in a network, in which rumor spreading obeys a time-slotted susceptible-infected model. Unlike existing approaches, our proposed algorithm identifies as sources those nodes, which when set as sources, result in the smallest dominant eigenvalue of the corresponding reduced nonbacktracking matrix deduced from message passing equations. We also propose a reduced-complexity algorithm derived from the previous algorithm through a perturbation approximation. Numerical experiments on synthesized and real-world networks suggest that these proposed algorithms generally have higher accuracy compared with representative existing algorithms.