I didn't say the circle was "around" Luke, but according to Philemon he and the other people mentioned along with him belonged to the same social circle, that of being Christians in close association with Paul.
By the way there is no claim in Philemon that Luke wrote anything or was a physician.
I am aware of that and have noted it in this thread. But I am starting to better appreciate Colossians, and if I had to guess who wrote it I would say Paul's close companion Timothy, and according to Philippians Timothy knew the same people that Luke did and the detail in Colossians that he was a physician fits with at least one and possibly two of them (including Timothy himself) suffering severe illnesses (along with the amount of illness and healing in Luke/Acts, regardless that the words used to describe it are also used in non-medical writings). So while nothing can be proven, I wouldn't dismiss the possibility that Luke was a physician and wrote or contributed to Luke/Acts.