Running times of our method on the model networks for each phase of the algorithm: (i) detecting 1-cut vertices and degree two vertices; (ii) predicting quasi-clique clusters; and (iii) running the genetic algorithm. We are reporting the average run time over three runs on each network. The implementation was tested on a Powermac G5 2 Ghz with 4 GB of RAM. Note that the genetic algorithm was run for a fixed amount of time, and the top scoring candidates achieved the quality as shown in Table 3. The times are shown in hh.mm.ss format.