  We study the \emph{picture space} $X^d(G)$ of all embeddings of a finite
graph $G$ as point-and-line arrangements in an arbitrary-dimensional projective
space, continuing previous work on the planar case. The picture space admits a
natural decomposition into smooth quasiprojective subvarieties called
\emph{cellules}, indexed by partitions of the vertex set of $G$, and the
irreducible components of $X^d(G)$ correspond to cellules that are maximal with
respect to a partial order on partitions that is in general weaker than
refinement. We study both general properties of this partial order and its
characterization for specific graphs. Our results include complete
combinatorial descriptions of the irreducible components of the picture spaces
of complete graphs and complete multipartite graphs, for any ambient dimension
$d$. In addition, we give two graph-theoretic formulas for the minimum ambient
dimension in which the directions of edges in an embedding of $G$ are mutually
constrained.
