Given the ever-increasing number of time-domain astronomical surveys, employing robust, interpretative, and automated data-driven classification schemes is pivotal. Based on graph theory, we present new data-driven classification heuristics for spectral data. A spectral classification scheme of Type II supernovae (SNe II) is proposed based on the phase relative to the maximum light in the V band and the end of the plateau phase. We utilize a compiled optical data set that comprises 145 SNe and 1595 optical spectra in 4000-9000 angstrom. Our classification method naturally identifies outliers and arranges the different SNe in terms of their major spectral features. We compare our approach to the off-the-shelf UMAP manifold learning and show that both strategies are consistent with a continuous variation of spectral types rather than discrete families. The automated classification naturally reflects the fast evolution of Type II SNe around the maximum light while showcasing their homogeneity close to the end of the plateau phase. The scheme we develop could be more widely applicable to unsupervised time series classification or characterization of other functional data.