  The classical distributed storage problem can be modeled by a k-uniform {\it
complete} hyper-graph where vertices represent servers and hyper-edges
represent users. Hence each hyper-edge should be able to recover the full file
using only the memories of the vertices associated with it. This paper
considers the generalization of this problem to {\it arbitrary} hyper-graphs
and to the case of multiple files, where each user is only interested in one, a
problem we will refer to as the graphical distributed storage problem (GDSP).
Specifically, we make progress in the analysis of minimum-storage codes for two
main subproblems of the GDSP which extend the classical model in two
independent directions: the case of an arbitrary graph with multiple files, and
the case of an arbitrary hyper-graph with a single file.
