HERMES: Persistent spectral graph software

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