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The Kuramoto model describes the collective dynamics of a system of coupledoscillators. An alpha-Kuramoto partition is a graph partition induced by theKuramoto model, when the oscillators include a phase frustration parameter. Weprove that every equitable partition is an alpha-Kuramoto partition, but thatthe converse does necessarily not hold. We give an exact characterisation ofalpha-Kuramoto bipartitions.

alpha-Kuramoto partitions: graph partitions from the frustrated Kuramoto model generalise equitable partitions