  We study the problem of Imbalance parameterized by the twin cover of a graph.
We show that Imbalance is XP parameterized by twin cover, and FPT when
parameterized by the twin cover and the size of the largest clique outside the
twin cover. In contrast, we introduce a notion of succinct representations of
graphs in terms of their twin cover and demonstrate that Imbalance is NP-hard
in the setting of succinct representations, even for graphs that have a twin
cover of size one.
