In a group of 7 friends, the only person who is not in a relationship. (The 6 friends and their partners + 13th wheel = 13) This character may be known as lone wolf, the bachelor, the free man. Most likely the coolest of the group, too cool for the opposite sex. The 13th wheel does not in anyway care that he/she is the 13th wheel. He/she's cool with it. Really fine with this.
Guy 1: Hey do you want to come hang out with me, Guy 2, Guy 3, Guy 4, Guy 5, and Guy 6? By the way our girlfriends are gonna be there too
You: No thanks man, I don't wanna be a 13th wheel.