  Given a finitely generated group $\Gamma$, a directed graph $\Lambda$, and a
map $R:\Lambda\to\Gamma$, we introduce the notion of an $(R,\Lambda)$-directed
Anosov representation. This is a weakening of the notion of Anosov
representations. Our main theorem gives a procedure to construct
$(R,\Lambda)$-directed Anosov representations using Fock-Goncharov positivity.
As an application of our main theorem, we construct large families of primitive
stable representations from $F_2$ to $\mathrm{PGL}(V)$, including non-discrete
and non-faithful examples.
