  Determining the key elements of interconnected infrastructure and complex
systems is paramount to ensure system functionality and integrity. This work
quantifies the dominance of the networks' nodes in their respective
neighborhoods, introducing a novel centrality metric, DomiRank, that integrates
local and global topological information via a tunable parameter. We present an
analytical formula and an efficient parallelizable algorithm for DomiRank
centrality, making it applicable to massive networks. From the networks'
structure and function perspective, nodes with high values of DomiRank
highlight fragile neighborhoods whose integrity and functionality are highly
dependent on those dominant nodes. Underscoring this relation between dominance
and fragility, we show that DomiRank systematically outperforms other
centrality metrics in generating targeted attacks that effectively compromise
network structure and disrupt its functionality for synthetic and real-world
topologies. Moreover, we show that DomiRank-based attacks inflict more enduring
damage in the network, hindering its ability to rebound and, thus, impairing
system resilience. DomiRank centrality capitalizes on the competition mechanism
embedded in its definition to expose the fragility of networks, paving the way
to design strategies to mitigate vulnerability and enhance the resilience of
critical infrastructures.
