Before revision:  Among other results,  we prove parameterized hardness (W[1]-hardness) regarding the size of the path sequence (solution size) for both variants, vertex- and edge-similarity.
After revision:  Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness (W[1]-hardness) regarding the size of the path sequence (solution size) for both variants, vertex- and edge-similarity.