A Graph-Theoretic Method to Representing a Concept Lattice

Concept lattices are indeed lattices. In this paper, we present a new relationship between lattices and graphs: given a binary relation I, we define an underlying graph D-I, and find out the constitution in the set of cover elements of the minimum element of the concept lattice of I using the properties of D-I. The following is to provide a way to establish a one-to-one correspondence between the set of covers of an element in the concept lattice and the set of covers of the minimum in a sublattice of the concept lattice. We apply the one-to-one correspondence to define a new underlying graph, and generate the elements of the lattice.