  Let $D$ be a connected weighted digraph. The relation between the vertex
weighted complexity (with a fixed root) of the line digraph of $D$ and the edge
weighted complexity (with a fixed root) of $D$ has been given in (L. Levine,
Sandpile groups and spanning trees of directed line graphs, J. Combin. Theory
Ser. A 118 (2011) 350-364) and, independently, in (S. Sato, New proofs for
Levine's theorems, Linear Algebra Appl. 435 (2011) 943-952). In this paper, we
obtain a relation between the vertex weighted complexity of the middle digraph
of $D$ and the edge weighted complexity of $D$. Particularly, when the weight
of each arc and each vertex of $D$ is 1, the enumerative formula of spanning
trees of the middle digraph of a general digraph is obtained.
