Fig. 1

False-positive “superbubble” returned by the algorithm of Sung et al. [7]. The directed 3-cycle a on the l.h.s. correctly yields the three subgraphs on two vertices as superbubbles. The graph b on the r.h.s., on the other hand, includes a as the only non-trivial strongly connected component. The vertices 1 and 3 have additional neighbors which are replaced by artificial nodes r and \(r'\), respectively. c, d are the corresponding DFS trees using an artificial source as root. Since no artificial source is present in a, a random vertex, here 1, is used as root. The correspond DAGs in e, f are constructed from duplicate copies of the DFS trees, augmented by source and sink vertices in e since these were lacking in c. Note that the same DAGs (g, h) are obtained for a and the non-trivial copy of a in b. Hence the same superbubbles are returned in both cases. While \(\langle 3,1\rangle\) is a valid result for a, it is a false positive for b since 3 is not a valid entrance and 1 is not a valid exit in b