The author applies the language of Joyal's species to enumeration problems of digraphs using the machinery of coloured species, see, e.g., the author and \textit{O. Nava} [J. Comb. Theory, Ser. A 64, No. 1, 102-129 (1993; Zbl 0787.05095)]. A species over digraphs is defined as a functor from the category of digraphs to the category of finite sets and bijections. Also, a matrix species is defined as an endofunctor of the category of digraphs, and a new set-theoretical operation between such species is introduced. As a result, an enriched version of the MacMahon master theorem is obtained. Other results are a new combinatorial proof of the all minors matrix tree theorem [see, e.g., \textit{S. Chaiken}, SIAM J. Algebraic Discrete Methods 3, 319-329 (1982; Zbl 0495.05018)] and a generalization of the BEST theorem [\textit{T. van Aardenne-Ehrenfest} and \textit{N. G. de Bruijn}, Simon Stevin 28, 203-217 (1951; Zbl 0044.38201)].