  Hyper-Wiener index was introduced as one of the main generalizations of the
well known Wiener index. Through the years properties of the Wiener index have
been extensively studied in both Mathematics and Chemistry. The Hyper-Wiener
index, although received much attention, is far from being thoroughly examined
due to its complex definition. We consider the local version of the
Hyper-Wiener index ($WW(G)$), defined as $ww_G(v)=\sum\limits_{u\in
V(G)}(d^2(u,v)+d(u,v))$ for a vertex $v$ in a graph $G$, in trees. For
established results on the Wiener index ($W(.)$), we present analogous studies
on $WW(.)$. In addition to interesting observations, some conjectures and
questions are also proposed.
