Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles defined by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we define an underlying graph G_R, and establish a one-to-one correspondence between the set of elements of the concept lattice of R and the set of minimal separators of G_R. We explain how to use the properties of minimal separators to define a sublattice, decompose a binary relation, and generate the elements of the lattice.