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How to divide a fully connected graph into similar subgraphs?

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I have a complete graph with symmetric weights (think about a set of cities with travel distance as edge cost) and I want to split the vertices into a fixed number of disjoint sets so that a an error function is optimized. The error function could for example be the maximum of the mean or maximal distance within the subgraphs.

I think that this should be a not too unusual problem, but I am missing the right search term to find the right algorithms or software packages.

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