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We study cluster synchronization of networks and propose a canonicaltransformation for simultaneous block diagonalization of matrices that we useto analyze stability of the cluster synchronous solution. Our approach hasseveral advantages as it allows us to: (1) decouple the stability problem intosubproblems of minimal dimensionality while preserving physically meaningfulinformation; (2) study stability of both orbital and equitable partitions ofthe network nodes and (3) obtain a parametrization of the problem in a smallnumber of parameters. For the last point, we show how the canonicaltransformation decouples the problem into blocks that preserve key physicalproperties of the original system. We also apply our proposed algorithm toanalyze several real networks of interest, and we find that it runs faster thanalternative algorithms from the literature.

Cluster Synchronization of Networks via a Canonical Transformation for Simultaneous Block Diagonalization of Matrices