I would calculate the distances from each point to all other points. Then sort the distances. Points that have a distance from each other that is below a threshold are considered Near. A group of points that is near to each other is a cluster.
The problem is that cluster may be clear to a human when he sees the graph, but does not have a clear mathematical definition. You need to define your near threshold, probably bu adjustuing it empirically until the result of your algorithm is (more or less) equal to what you perceive as being clustered.
