Detecting information source in viral spreading has important applications such as to root out the culprit of a rumor spreading in online social networks. In particular, given a snapshot observation of the network topology of nodes having the rumor, how to accurately identify the initial source of the spreading? In the seminal work [Shah et el. 2011], this problem was formulated as a maximum likelihood estimation problem and solved using a rumor centrality approach for graphs that are degree-regular trees. The case of graphs with cycles is an open problem. In this paper, we address the maximum likelihood estimation problem by a generalized rumor centrality for spreading in unicyclic graphs. In particular, we derive a generalized rumor centrality that leads to a new graph-theoretic design approach to inference algorithms.