A set  is eccentric hub set of a graph G if H is a hub set of G and also every  has an eccentric vertex in H. The minimal eccentric hub set with minimum cardinality is called minimum eccentric hub set. Its cardinality is eccentric hub number of G, denoted by  In this paper, we deduce some results and bounds on this parameter. Further, we have studied about total number of minimum eccentric hub sets and eccentric hub graphs.

hub number, eccentric hub number, eccentric hub graph.