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

On the spectral radius of simple digraphs with prescribed number of arcs