A labeling of the vertices of a graph with distinct natural numbers induces a natural labeling of its edges: the label of an edge (x,y) is the absolute value of the difference of the labels of x and y. We say that a labeling of the vertices of a graph of order n is minimally k-equitable if the vertices are labeled with 1,2... n and in the induced labeling of its edges, every label either occurs exactly k times or does not occur at all. In this paper, we prove that Butterfly and Benes networks are minimally 2τ- equitable where τ is the dimension of the networks.