Topological entropy serves as a fundamental invariant in dynamical systems, quantifying the complexity of orbits under continuous maps. In this talk, we will explore a critical example: investigating the conditions under which the topological entropy of the shift map is well-defined and demonstrating that it equals the logarithm of the spectral radius of the incidence matrix. Utilizing the Perron–Frobenius theorem, we derive essential insights into the spectral radius of primitive matrices. By having permutation matrices act on the incidence matrix, we transform it into a specific block matrix form, enabling us to extend results from the special case of primitive incidence matrices to the general case.