Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In this paper we use a method, which applies group theory to graph theory, to improving mathematically computation of the (first) edge-hyper Wiener index in certain graphs. We give also upper and lower bounds for the (first) edge-hyper Wiener index of a graph in terms of its size and Gutman index. Also we investigate products of two or more graphs and compute the second edge-hyper Wiener index of the some classes of graphs. Our aim in last section is to find a relation between the third edge-hyper Wiener index of a general graph and the hyper Wiener index of its line graph. of two or more graphs and compute edge-hyper Wiener number of some classes of graphs.