Graph component question

Hi all, finding edges of cycles in a directed graph is a solved problem and done by the strong_components algorithm. Is there also any a good solution for finding the path (= the exact sequence of vertices) that encloses a strong component? (Note that in a strong component there can be also smaller subcycles that are not of interest.) With other words: I want to find the way through a strong component that visits all its edges. Thanks in advance! Stefan