  A unitary equivalence class of endomorphisms of a unital C$^{*}$-algebra
${\cal A}$ is called a {\it sector} of ${\cal A}$. We introduced permutative
endomorphisms of the Cuntz algebra ${\cal O}_N$ in the previous work. Branching
laws of permutative representations of ${\cal O}_N$ by them are computed by
directed regular graphs. In this article, we classify sectors associated with
permutative endomorphisms of ${\cal O}_N$ by their graph invariants concretely.
