I have a question regarding Rayleigh quotient. It's well known that maximal eigenvalue can be found by
$\lambda_{\max}(M)=\max_{x\neq 0}\frac{x^{T}Mx}{x^{T}x}.$
Using this how to prove that $\lambda_{\max}(A)$ is placed between average degree $\frac{1}{n}\sum d_{i}$ and maximal degree $\max d_i$.
Thanks