There is definitely added reason to remain friends
Just because people break up doesn't mean you have to go separate ways. For the person you have the original connection with it could be awkward, and that's kinda the reality they've created - they can't always have the luxury of a clean break, I mean, THEY introduced this person to your lives!
My sister is still a bit dark on me for staying friends with her ex BF. She went OS and told me to hang out with her BF to go surfing and said he was a great guitarist. So, we surfed together and then started making music together...and formed a lovely little acoustic duo that lots of people love to come and listen to...my bad? Don't think so, it's just one of those things!