In the literature, it is sometimes indicated that network with high value of largest eigenvalue (either adjacency matrix or its Laplacian counterpart) are more robust against link/node removals. However, these statements are usually NOT accompanied with references.

I am looking for some explanation on why is this so? Or pointers to some work that investigate/explain this.

I wonder if this statement is simply the result of difference between link density? I doubt its so simplistic. Is there any study on network robustness comparing networks with same link density but different largest eigenvalues (or spectral radius)?