  The Littlewood--Offord problem concerns the number of subsums of a set of
vectors that fall in a given convex set. We present a discrete variation of the
Littlewood--Offord problem and then utilize that for finding the the maximum
order of graphs with given rank or corank. The rank of a graph $G$ is the rank
of its adjacency matrix $A(G)$ and the corank of $G$ is ${\rm rank}(A(G)+I)$.
