# Cluster data points by distance between clusters

I have a load of point data in 3D, and I wish to cluster them like so:

• Each cluster contains points all of which are at most distance $d$ from another point in the cluster.
• All points in two distinct clusters are at least distance $d$ from each other.

The distances used are Euclidean distances.

Is this a well known clustering algorithm? If so, what is is called? Thanks.

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Create a graph in which the points are nodes and two points are connected with an edge if and only if they lie within distance $d$ of each other. Stated in these terms, your criteria become