  In this paper, we study graphical conditions for structural controllability
and accessibility of drifted bilinear systems over Lie groups. We consider a
bilinear control system with drift and controlled terms that evolves over the
special orthogonal group, the general linear group, and the special unitary
group. Zero patterns are prescribed for the drift and controlled dynamics with
respect to a set of base elements in the corresponding Lie algebra. The drift
dynamics must respect a rigid zero-pattern in the sense that the drift takes
values as a linear combination of base elements with strictly non-zero
coefficients; the controlled dynamics are allowed to follow a free zero pattern
with potentially zero coefficients in the configuration of the controlled term
by linear combination of the controlled base elements. First of all, for such
bilinear systems over the special orthogonal group or the special unitary
group, the zero patterns are shown to be associated with two undirected or
directed graphs whose connectivity and connected components ensure structural
controllability/accessibility. Next, for bilinear systems over the special
unitary group, we introduce two edge-colored graphs associated with the drift
and controlled zero patterns, and prove structural controllability conditions
related to connectivity and the number of edges of a particular color.
