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 $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...
