On the Usage of Graph Spectra in Protein Structural Similarity

The spectrum of a matrix M is the multiset that contains all the eigenvalues of M. If M is a matrix obtained from a graph G, then the spectrum of M is also called the graph spectrum of G. If two graphs has the same spectrum, then they are cospectral (or isospectral) graphs. In this paper, we compare four spectra of matrices to examine their accuracy in protein structural comparison. These four spectra are derived from adjacency matrix, Laplacian matrix, signless Laplacian matrix, and Seidel adjacency matrix. In the analysis of protein subunits, corroborating protein database CATH, SCOP, and RCSB PDB, results suggest that when Seidel adjacency matrix is applied, it performs a preferable outcome in protein complex structures. In addition, the proposed method outperforms than typical RMSD geometric metric distance. This graph-theoretic approach offers a practical direction for protein subunit comparison.