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Sorting coordinates to group them into "places".

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I have a large matrix representing points in a Euclidean plane. I need to group together all points which are within 100meters of each other and call these points the "same place."
I have created a 15000x15000 inter-point distance matrix that has the distance between each point and any other point. I need to figure out a way to loop through this data and group together all points within 100m of each other and return something like "Points 1, 5, 312, 534, and 10452 are all within 100m of each other so this is Place 1."
Any ideas? I am quite stuck on this problem.

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