  Persistent homology (PH) is one of the most popular tools in topological data
analysis (TDA), while graph theory has had a significant impact on data
science. Our earlier work introduced the persistent spectral graph (PSG) theory
as a unified multiscale paradigm to encompass TDA and geometric analysis. In
PSG theory, families of persistent Laplacians (PLs) corresponding to various
topological dimensions are constructed via a filtration to sample a given
dataset at multiple scales. The harmonic spectra from the null spaces of PLs
offer the same topological invariants, namely persistent Betti numbers, at
various dimensions as those provided by PH, while the non-harmonic spectra of
PLs give rise to additional geometric analysis of the shape of the data. In
this work, we develop an open-source software package, called highly efficient
robust multidimensional evolutionary spectra (HERMES), to enable broad
applications of PSGs in science, engineering, and technology. To ensure the
reliability and robustness of HERMES, we have validated the software with
simple geometric shapes and complex datasets from three-dimensional (3D)
protein structures. We found that the smallest non-zero eigenvalues are very
sensitive to data abnormality.
