FriendCountList

FriendCountList[conlist] gives a list of the type {{1, {1, 4}}, {2, {2, 3, 6}}, {4, {5, 7}}}, with the meaning the point 1 and 4 are connected to one other point each, the points 2, 3 and 6 are connected to two points each and the points 5 and 7 are connected to four points each.