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When evaluating clustering algorithms for networks, we have well-established metrics like Modularity and Surprise for evaluating the quality of the resulting partition.

If we then embed our graph (well) in a metric space, it becomes much easier to compute distances and communities using geometric algorithms on the points, at the cost of losing our link structure. Therefore, given a partitioning of the points in the metric space (into, say, k clusters) are there any well-established metrics for computing the quality of the clusters?

And if such metrics exist, can we say anything about what embedding/clustering methods are likely to yield clusters that yield similar results when moving from a graph to its embedding?

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