Comic edge, parallel tracks between

The film is slated to release in October, and he doesn't have a title yet. The working title of this movie is 'Dil Dar-ba-Dar...'
Mishra's latest has an impressive line up of stars like Irrfan Khan, Arunoday Singh, Chitrangadha Singh and Aditi Rao. Sudhir is confused about two titles and cannot decide on one. So he has decided to seek the help of his audience.
He has posted a very crucial scene from his forthcoming movie on his face book profile page. He wants the audiences to see it and decide for themselves.
"While the working title of the film was 'Dil Dar-ba-Dar', over the weeks of editing my team was equally divided between that and 'Yeh Saali Zindagi', hence the dilemma. Incidentally, both these titles also represent equally strong songs in the film, so I decided to release a clip from the film online to give an idea of the film's content and style, and ask my friends for their advice on the apt title," the director says.
The film is a romantic thriller with a comic edge. It is a love story that has parallel tracks between Irfan Khan, Chitrangadha Singh, Arunoday Singh and Aditi Rao's characters.

Please explain to me the emboldened parts.
Though I know "edge" generally means "advantage" and "comic" means "comedy films".
Source : http://www.dnaindia.com/entertainment/report_sudhir-mishra-seeks-help-for-deciding-title-of-next-film_1407165