Divide GIS points into groups of points that are close together

Question

You have a set of coordinates that need to be divided into groups close to each other.

Work with Python regarding PostgreSQL database. I figured out which solution would work, but then I realized that I was probably reinventing the wheel again. Are there libraries that I can use to accomplish this without having my own solution?

Example:

Answer 1

GIS SE has two good solutions to this question, implemented directly in PostGIS:

Spatial Clustering with PostGIS

You can also find helpful hints in answers to:

How to identify clusters in vector point data?