The edge dominating graph ED(G) of a graph G = (V,E) is a graph with V (ED(G))=E(G)∪ S(G), where S(G) is the set of all minimal edge dominating sets of G with two vertices u, v ∈ V (ED(G)) adjacent if u ∈ E and v is a minimal edge dominating set of G containing u. In this paper, we establish the bounds on order and size, diameter and vertex(edge) connectivity.