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We consider special multiclass spectral, discrepancy, degree, and codegreeproperties of expanding graph sequences. As we can prove equivalences andimplications between them and the definition of the generalized quasirandomnessof Lov\'asz--S\'os (2008), they can be regarded as generalized quasirandomproperties akin to the equivalent quasirandom properties of the seminalChung--Graham--Wilson paper (1989) in the one-class scenario. Since theseproperties are valid for certain deterministic graph sequences, irrespective ofstochastic models, the partial implications also justify for law-dimensionalembedding of large-scale graphs and for discrepancy minimizing spectralclustering.

Generalized quasirandom properties of expanding graph sequencesedding