Topological analysis of eigenvectors of the adjacency matrices in graph theory: The concept of internal connectivity

[[abstract]]The topological properties of eigenvectors of adjacency matrices of a graph have been analyzed. Model systems studied are n-vertex-m-edge (n-V-m-E) graphs where n = 2–4, m = 1–6. The topological information contained in these eigenvectors is described using vertex-signed and edge-signed graphs. Relative ordering of net signs of edge-signed graphs is similar to that of eigenvalues of the adjacency matrix. This simple analysis has also been applied to naphthalene, anthracene and pyrene. It provides a sound basis for the application of graph theory to molecular orbital theory.[[fileno]]2010321010017[[department]]化學