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Determining the key elements of interconnected infrastructure and complexsystems is paramount to ensure system functionality and integrity. This workquantifies the dominance of the networks' nodes in their respectiveneighborhoods, introducing a novel centrality metric, DomiRank, that integrateslocal and global topological information via a tunable parameter. We present ananalytical formula and an efficient parallelizable algorithm for DomiRankcentrality, making it applicable to massive networks. From the networks'structure and function perspective, nodes with high values of DomiRankhighlight fragile neighborhoods whose integrity and functionality are highlydependent on those dominant nodes. Underscoring this relation between dominanceand fragility, we show that DomiRank systematically outperforms othercentrality metrics in generating targeted attacks that effectively compromisenetwork structure and disrupt its functionality for synthetic and real-worldtopologies. Moreover, we show that DomiRank-based attacks inflict more enduringdamage in the network, hindering its ability to rebound and, thus, impairingsystem resilience. DomiRank centrality capitalizes on the competition mechanismembedded in its definition to expose the fragility of networks, paving the wayto design strategies to mitigate vulnerability and enhance the resilience ofcritical infrastructures.

DomiRank Centrality: revealing structural fragility of complex networks via node dominance