Theoretical Analysis of DomiRank Centrality: Automorphism, Entropy, and Graph Transformations
This study addresses the unclear theoretical mechanisms of the DomiRank algorithm under graph symmetry, information entropy, and topological transformations by integrating dynamical systems, graph theory, spectral analysis, and information-theoretic frameworks. By establishing a connection between node importance dynamics and graph automorphisms, we prove that regular graphs maximize entropy, reveal the monotonically decreasing effect of the competition parameter on entropy, and derive eigenvalue conditions on the degree vector for distributional invariance. Empirical evaluations on real-world networks confirm that DomiRank serves as a tunable complement to principal eigenvector centrality, exhibiting distinct advantages under strong competition regimes. These findings provide a rigorous theoretical foundation for identifying critical nodes in complex networks.