Before revision:  Also, an efficient algorithm based on Gomory-Hu tree for calculating ANF is presented. Finally , this paper compares ANF with eight representative existing metrics, showing that each metric has its own characteristics  in measuring network robustness and hence they are not equivalent.
After revision:  Also, an efficient algorithm based on Gomory-Hu trees. Thus, with ANF intrinsically considering global network topologies, ANF is unveiled to be a new robustness metric satisfying those three properties. Moreover , this paper compares ANF with eight representative existing metrics, showing that each metric has its own characteristics in measuring network robustness and hence they are not equivalent.