In this paper, we present a new relationship between fuzzy concept lattice and fuzzy graph. Given a fuzzy binary relation, we define an underlying fuzzy graph, and establish a new relation between the set of elements of the fuzzy concept lattice built from the fuzzy relation and the set of minimal disconnections of the associated fuzzy graph. This link is important from the point of view of application and computation. © 2009 Elsevier B.V. All rights reserved.