Before revision:  This paper proposes a robustness metric called Average Network Flow (ANF) , which satisfies these three properties, but is not based on graph spectra. Also, an efficient algorithm based on Gomory-Hu tree for calculating ANF is presented.
After revision:  This paper proposes a robustness metric called Average Network Flow (ANF) as a robustness metric, and proves that it increases strictly, and gives an algorithm to compute ANF with a quadratic complexity by leveraging Gomory-Hu tree for calculating ANF is presented.