Net signs of molecular graphs: Dependence of molecular structure

The concept of internal connectivity associates to each eigenvector of the molecular graph a graph with signed edges. We show that the respective edge signs can be deduced without knowing the graph eigenvectors. The dependence of the edge signs on molecular structure is elucidated. The sign of an edge whose end vertices are ν_r and ν_s is found to be the result of separate interactions through all paths connecting the vertices ν_r and ν_s. The analysis of the edge signs is particularly simple in the case of acyclic systems. © 1994 John Wiley & Sons, Inc.