Various types of genome and gene similarity networks along with their characteristics have been increasingly used for retracing different kinds of evolutionary and ecological relationships. Here, we present a new polynomial time algorithm and the corresponding software (BRIDES) to provide characterization of different types of paths existing in evolving (or augmented) similarity networks under the constraint that such paths contain at least one node that was not present in the original network. These different paths are denoted as Breakthroughs , Roadblocks, Impasses, Detours, Equal paths, and Shortcuts. The analysis of their distribution can allow discriminating among different evolutionary hypotheses concerning genomes or genes at hand. Our approach is based on an original application of the popular shortest path Dijkstra's and Yen's algorithms.