  The harmonic index of a graph $G$ is defined as the sum of weights
$\frac{2}{deg(v) + deg(u)}$ of all edges $uv$ of $E (G)$, where $deg (v)$
denotes the degree of a vertex $v$ in $V (G)$. In this note we generalize
results of [L. Zhong, The harmonic index on graphs, Appl. Math. Lett. 25
(2012), 561--566] and establish some upper and lower bounds on the harmonic
index of $G$.
