  In 2010, Hernandez and Leclerc studied connections between representations of
quantum affine algebras and cluster algebras. In 2019, Brito and Chari defined
a family of modules over quantum affine algebras, called Hernandez-Leclerc
modules. We characterize the highest $\ell$-weight monomials of
Hernandez-Leclerc modules. We give a non-recursive formula for $q$-characters
of Hernandez-Leclerc modules using snake graphs, which involves an explicit
formula for $F$-polynomials. We also give a new recursive formula for
$q$-characters of Hernandez-Leclerc modules.
