A vertex-degree-based (VDB, for short) topological index $\phi$ induced by the numbers $\left\{{\phi }_{ij}\right\}$ was recently defined for a digraph D, as ${\displaystyle \phi \left(D\right)=\frac{1}{2}\sum _{uv}{\phi }_{d_u^{+}{d}_v^{-}},}$ where $d_u^{+}$ denotes the out-degree of the vertex $u,$$d_v^{-}$ denotes the in-degree of the vertex $v,$ and the sum runs over the set of arcs $uv$ of D. This definition generalizes the concept of a VDB topological index of a graph. In a general setting, we find sharp lower and upper bounds of a symmetric VDB topological index over ${\mathcal{D}}_n$, the set of all digraphs with n non-isolated vertices. Applications to well-known topological indices are deduced. We also determine extremal values of symmetric VDB topological indices over $\mathcal{OT}\left(n\right)$ and $\mathcal{O}\left(G\right)$, the set of oriented trees with n vertices, and the set of all orientations of a fixed graph G, respectively.