Discussing this thought with a few of my friends made me realise that it is was not as simple as it seemed on the surface. During the course of a relationship be it your boyfriend/girlfriend, spouse or even friends; you tend to meet several other people that might be your friends or your partner's. Now, these are what we label as 'mutual friends'. They have a very interesting role to play as even after the relation ends on a 'not so happy note', they are the ones who keep the two sides bonded through a thin social glue. Just because you found these friends during the relationship and they might just happen to be friends of your partner doesn't really mean that once the relation ends so do these new friendships. As a matter of fact many times they can be the ones that help you get over the bad phase and start afresh. No doubt that sometimes because of your 'ex partner'; situations with mutual friends may get sticky, awkwardness may also prevail. But, these are the friends who will remain through all the thick and thin.
Sometimes, you might just find a love interest in one of these mutual friends because they have seen you through your worst and best phases. They probably understand your emotional psyche a lot better. So, the point that I am trying to make here is that it doesn't really matter if that relation is over because it was never really worth the effort, (of course if it would have been; you wouldn't have been alone right now) and the worst thing would now be to also lose these new friends that you have made.
Keep them close.