Here is a method extracting the edges, which are in the group. For each point and each neighbour you can check, if the distance is close enough to one of these edges. It is probably necessary, to collect all incident edges for each point, because there can be more than one edge, which is in the group and close enough to the point (especially if the point is an original point and it has multiple edges, which are in the group). The midpoint of both points should be close enough to one of these edges from both points, If this is the case, the edge should be in the group.
group_if_small_dist.hipnc