An elementary circuit (or tie) is a subgraph of a graph and the set of edges in this subgraphis called an elementary tieset. The distance d(ei, ej ) between two edges in an undirected graph is defined as the minimum number of edges in a tieset containing ei and ej . The eccentricity ετ (ei) of an edge ei is ετ (ei) = maxej∈Ed(ei, ej ). In this paper, we have introduced the edge - self centered and edge - eccentric graph of a graph and have obtained results on these concepts
