Robustness quantification of hierarchical complex networks under targeted failures

Robustness is one of the key properties in complex networks to ensure the expected level of performance and service availability in case of perturbations and failures. Network robustness is generally quantified using various classical metrics. However, whether the robustness quantification of the networks in various types of failures can be proved to be valid or not? Moreover, how does the hierarchy of a network impacts the robustness, is still not a well-explored domain. This paper presents the robustness quantification of hierarchical complex networks under targeted attacks. We analyze ten different real-world networks with varying graph characteristics using the classical robustness metrics. The level of the hierarchy of the considered networks is computed using the Global Reaching Centrality (GRC) measure. To depict the targeted attacks, we remove (decommission) specific network nodes based on the nodal degree and node betweenness centrality. Moreover, to compare various networks with varying size and characteristics, we employ deterioration strategy to evaluate the effect of the failures on hierarchical networks. Our results reveal a strong relationship between hierarchy and robustness of the networks. Moreover, the presented results reveal that the robustness inferences based on the classical robustness measures may be inaccurate. It can be inferred from the analysis that the classical robustness metrics may not be able to quantify the structural robustness of hierarchical complex networks appropriately, which lay down a need for new robustness metrics for robustness quantification.