DomiRank Centrality reveals structural fragility of complex networks via node dominance

Definition and interpretation of DomiRank Centrality

We define DomiRank centrality, denoted \({{{{{{{\boldsymbol{\Gamma }}}}}}}}\in {{\mathbb{R}}}_{N\times 1}\), as the stationary solution of the following dynamical process

$$\frac{d{{{{{{{\boldsymbol{\Gamma }}}}}}}}(t)}{dt}=\alpha A(\theta {{{{{{{{\boldsymbol{1}}}}}}}}}_{N\times 1}-{{{{{{{\boldsymbol{\Gamma }}}}}}}}(t))-\beta {{{{{{{\boldsymbol{\Gamma }}}}}}}}(t),$$

(1)

where \(A\in {{\mathbb{R}}}_{N\times N}\) is the adjacency matrix of the network \({{{{{{{\mathcal{N}}}}}}}}\) and

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