An eigenvalue localization theorem for stochastic matrices and its   application to Randi\'c matrices
  A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randi\'c matrix of a connected graph. 
Anirban Banerjee, Ranjit Mehatari
math.CO