by Leon da Silva
Spectral graph theory is the branch of graph theory which explores facts, structures and other properties of a graph based off of information gathered from its adjacency matrix, Laplacian matrix and other invariants. Eigenvalues also play a large role in establishing bounds to properties of graphs.
Spectral graph theory not only relates closely to other areas of mathematics, but also to seemingly unrelated disciplines. For example, exploring the eigenvalues of a graph of a molecular structure can give insight into its stability. Also, spectral graph theory concepts are used in quantum mechanics to “minimize energies in Hamiltonian systems.”
This paper will attempt to establish a framework for applying spectral graph theory into a finance and provide some preliminary results.