Outlier detection with alphashape

Is there a good way to judge if the point is outlier with alphashape ? For example, if the point has only one connection or neighbor ? The point is, the outlier is in the alpha distance but in the example it has only 3 connections while other points has more. I know i can reduce the distance and eliminate that point but it could have other side effects. My real intention is to really find how many connection each point has.

Thanks