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We define a class of Euclidean distances on weighted graphs, enabling toperform thermodynamic soft graph clustering. The class can be constructed formthe "raw coordinates" encountered in spectral clustering, and can be extendedby means of higher-dimensional embeddings (Schoenberg transformations).Geographical flow data, properly conditioned, illustrate the procedure as wellas visualization aspects.

Euclidean Distances, soft and spectral Clustering on Weighted Graphs