Infrastructure networks such as the Internet backbone and power grids are essential for our everyday lives. With the prevalence of cyber-attacks on them, measuring the robustness of infrastructure networks has become an important issue. To date, many robustness metrics have been proposed for this purpose . It is desirable for a robustness metric to possess the following three properties: considering global network topologies, strictly increasing upon link additions, and having a quadratic complexity in terms of the number of nodes on sparse networks. Currently, most of the metrics satisfying these three properties are based on graph spectra. 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. 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. Moreover, by focusing our comparisons on the scenarios in which network topologies change while preserving the same numbers of nodes and links, some specific observations on robustness metrics are reported.
Infrastructure networks such as the Internet backbone and power grids are essential for our everyday lives. With the prevalence of cyber-attacks on them, measuring their robustness has become an important issue. To date, many robustness metrics have been proposed . It is desirable for a robustness metric to possess the following three properties: considering global network topologies, strictly increasing upon link additions, and having a quadratic complexity in terms of the number of nodes on sparse networks. This paper proposes to use 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 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 seven existing representative metrics, showing that each metric has its own characteristics , so there is no silver bullet in measuring network robustness and it is recommended to apply several metrics together to gain a comprehensive view. Finally, by experimenting on the scenarios in which network topologies preserve the same numbers of nodes and links, some interesting behaviors of robustness metrics are reported.
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