  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 $\overset{\circ}{\mathrm {A}}$. 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 characterisation of other functional
data.
