how do I cluster a list of geographic points by distance?

Question

I have a list of points P=[p1,...pN] where pi=(latitudeI,longitudeI).

Using Python 3, I would like to find a smallest set of clusters (disjoint subsets of P) such th

Answer 1

Here is a solution that seems correct and will behave O(N^2) worst case and better depending on the data:

def my_cluster(S,distance):
    coords=set(S)
    C=[]
    while len(coords):
        locus=coords.pop()
        cluster = [x for x in coords if vincenty(locus,x).km <= distance]
        C.append(cluster+[locus])
        for x in cluster:
            coords.remove(x)
    return C

NOTE: I am not marking this as an answer because one of my requirements is that it be a smallest set of clusters. My first pass is good but I haven't proven that it is a smallest set.

The result (on a larger set of points) can be visualized as follows: