  Albertson defined the irregularity of a graph $G$ as
$irr(G)=\sum\limits_{uv\in E(G)}|d_G(u)-d_G(v)|$. For a graph $G$ with $n$
vertices, $m$ edges, maximum degree $\Delta$, and $d=\left\lfloor \frac{\Delta
m}{\Delta n-m}\right\rfloor$, we show $$irr(G)\leq
d(d+1)n+\frac{1}{\Delta}\left(\Delta^2-(2d+1)\Delta-d^2-d\right)m.$$
