We investigate some topological and spectral properties of
Erd\H{o}s-R\'{e}nyi (ER) random digraphs D(n,p). In terms of topological
properties, our primary focus lies in analyzing the number of non-isolated
vertices Vx(D) as well as two vertex-degree-based topological indices: the
Randi\'c index R(D) and sum-connectivity index χ(D). First, by
performing a scaling analysis we show that the average degree ⟨k⟩ serves as scaling parameter for the average values of Vx(D), R(D)
and χ(D). Then, we also state expressions relating the number of arcs,
spectral radius, and closed walks of length 2 to (n,p), the parameters of ER
random digraphs. Concerning spectral properties, we compute six different graph
energies on D(n,p). We start by validating ⟨k⟩ as the scaling
parameter of the graph energies. Additionally, we reformulate a set of bounds
previously reported in the literature for these energies as a function (n,p).
Finally, we phenomenologically state relations between energies that allow us
to extend previously known bounds