  This paper presents a sharp upper bound for the spectral radius of simple
digraphs with described number of arcs. Further, the extremal graphs which
attain the maximum spectral radius among all simple digraphs with fixed arcs
are investigated. In particular, we characterize all extremal simple digraphs
with the maximum spectral radius among all simple digraphs with arcs number
$e=2{k\choose 2}+t$ and $k>4t^4+4$.
