  In this paper we introduce $F$-invariant in cluster algebras using
tropicalization, which is an analog of the $E$-invariant introduced by
Derksen-Weyman-Zelevinsky in the additive categorification of cluster algebras
and the $\mathfrak{d}$-invariant introduced by Kang-Kashiwara-Kim-Oh in the
monoidal categorification of (quantum) cluster algebras.
