A note on almost regular matrices
A symmetric matrix \({\mathbf A}= [a_{ij}]\) of order \(n\), all the entries of which are nonnegative and all the row sums \(d_1,d_2,\dots, d_n\) of which are positive, is said to be almost regular if there is a positive number \(r\) such that \(d_i d_j= r^2\) if \(a_{ij}> 0\). This note gives necessary and sufficient conditions for almost regular matrices and discusses some related matters.
scientific article; zbMATH DE number 803732