Circularity of the numerical range of a nonnegative matrix (Q2712465)

Let \(A\) be a complex square matrix, the set \(F(A)=\{x^*Ax \mid x\in\mathbf C^n, x^*x=1\}\) is called the numerical range of \(A\), where \(^*\) is the operator of complex conjugation followed by transposition. By using graph theory and classical results on nonnegative matrices, the authors obtain a necessary and sufficient condition such that a nonnegative matrix has a circular disk centered at the origin as its numerical range.