Dyad algebra and multiplication of graphs. II. Undirected graphs

In paper I abstract vectors |e>, their adjoints <e|, dyads such as |e><e|, and abstract linear operators were related to graphs which are in general directed. With an Hermitian operator one gets equivalence classes of undirected graphs with or without loops and multi-lines. The present paper II gives rules for the multiplication of such graphs based on their underlying dyad algebra. The results may be used in the evaluation of the outcome of successive applications of operators for observables as in the case of the powers of a one-electron Hamiltonian in the method of moments, or in using projection operators, electron density, and the like.