Some new inequalities on spectral radius for the Hadamard product of nonnegative matrices

In this paper, we develop a series of inequalities characterizing the upper bound on spectral radius for the Hadamard product of nonnegative matrices by using the theory of directed graph. Meanwhile, the theoretical comparisons between the newly obtained upper bounds and some existing results are also investigated, and show that some newly obtained upper bounds theoretically improve some existing ones. To further illustrate the effectiveness and sharpness of the main results, some numerical examples are considered.