  Understanding biological network dynamics is a fundamental issue in various
scientific and engineering fields. Network theory is capable of revealing the
relationship between elements and their propagation; however, for complex
collective motions, the network properties often transiently and complexly
change. A fundamental question addressed here pertains to the classification of
collective motion network based on physically-interpretable dynamical
properties. Here we apply a data-driven spectral analysis called graph dynamic
mode decomposition, which obtains the dynamical properties for collective
motion classification. Using a ballgame as an example, we classified the
strategic collective motions in different global behaviours and discovered
that, in addition to the physical properties, the contextual node information
was critical for classification. Furthermore, we discovered the label-specific
stronger spectra in the relationship among the nearest agents, providing
physical and semantic interpretations. Our approach contributes to the
understanding of principles of biological complex network dynamics from the
perspective of nonlinear dynamical systems.
