  This paper considers the topological degree of $G$-shifts of finite type for
the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has
a finite representation and the relationships among the generators of $G$ are
determined by a matrix $A$, the coefficients of the characteristic polynomial
of $A$ are revealed as the number of children of the graph. After introducing
an algorithm for the computation of the degree, the degree spectrum, which is
finite, relates to a collection of matrices in which the sum of each row of
every matrix is bounded by the number of children of the graph. Furthermore,
the algorithm extends to $G$ of finite free-followers.
