The semientire edge dominating graph Eed(G) of a graph G=(V, E) is a graph with the vertex set E S where S is the set of
all minimal edge dominating sets G and with two vertices u,v E S adjacent if u,v F where F is a minimal edge dominating set in S or u E and v=F is a minimal edge dominating set of G containing u. In this paper, a characterization is given for graphs G for which Eed(G) is connected. Further, some new results are established relating to this new graph.