  For a quantum many-body problem, effective Hamiltonians that give exact
eigenvalues in reduced model space usually have different expressions, diagrams
and evaluation rules from effective transition operators that give exact
transition matrix elements between effective eigenvectors in reduced model
space. By modifying these diagrams slightly and considering the linked diagrams
for all the terms of the same order, we find that the evaluation rules can be
made the same for both effective Hamiltonian and effective transition operator
diagrams, and in many cases it is possible to combine many diagrams into one
modified diagram. We give the rules to evaluate these modified diagrams and
show their validity.
