What is a hero, and who is the real hero of The Godfather?

The definition of "hero" is "a man of distinguished courage or ability, admired for his brave deeds and noble qualities" (Dictionary.com).  Another definition using Classical Mythology is "a being of godlike prowess and beneficence who often came to be honored as a divinity" (Dictionary.com). This early into "The Godfather", it is hard to distinguish the hero of the movie, but using those two definitions, Vito Corleone, known as The Don and The Godfather, is the hero of the movie.  

It is intriguing that the leader of a gang could be the hero of the movie, but using the definitions, it is true. Because he is so powerful, many people would like him dead, and it makes him courageous for even showing his face in public.  

The definition of a "hero" using Classical Mythology is the most interesting, and connects well with The Don.  The fact that his nickname is The Godfather, and a hero is "a being of godlike prowess", it is evident that Coppola wanted to portray The Godfather as a hero in his movie.