that a stable set bundle forms a clique class in the quotient graph. Considered the other way around, adding a false twin to every vertex of a clique class yields a stable set bundle. Following Lemma \[lem:SSCmitgleichemgewicht\] the vertices of a stable set bundle are pairwise mds-exchangeable and, therefore, every equidominating function is constant on a stable set bundle.

Now, regarding the question whether two vertices can have the same weight in an equidominating structure, the last open question is: can vertices of a clique class or a singleton class have the same weight as its neighboring clique class or singleton class? The answer is yes: there can be a clique, that is not a clique class, whose vertices are pairwise mds-exchangeable.

Let $G$ be a graph and $\mathcal{C}$ an inclusion-wise maximal clique of pairwise mds-exchangeable vertices that contains at least two twin classes. Then $\mathcal{C}$ is called a *clique bundle*.

Upon first reading it seems a little bit odd to define clique bundles exactly as what we are looking for: pairwise mds-exchangeable vertices of possibly different twin classes. However, the crucial thing here is that we can identify clique bundles efficiently (see Algorithm \[alg:adjacentmdsexchangeable\]). We require at least two 