Renormalization of a graph adjacency matrix

Question

I know for graph adjacency matrix $A$ and degree matrix $D$, the eigenvalues of $I+D^{-1/2}AD^{-1/2}$ are in $[0,2]$ and repeated use of this as a filter will cause the numerical insatbility. I also know that to overcome from this a renormalization technique is used to get the expression like $\tilde{D}^{-1/2}\tilde{A}\tilde{D}^{-1/2}$ where $\tilde{A}=A+I$ and $\tilde{D}=diag\left\{\Sigma_j \tilde{A}_{i,j} \right\}$. But what I don't understand is how these two expressions:$I+D^{-1/2}AD^{-1/2}$ and $\tilde{D}^{-1/2}\tilde{A}\tilde{D}^{-1/2}$ are equivalent.