TripRank: A centrality metric based on dynamic competition of geometric–topological structures for influential nodes identification

Identifying influential nodes is fundamental for understanding network robustness and controlling spreading dynamics. Existing centrality metrics often rely on static, linear combinations of local and global indicators, failing to capture the complex, non-linear interplay between geometric cohesion and topological connectivity. To address this, we propose TripRank, a centrality metric that models node influence by simulating a dynamic competition between geometric factors and topological features. Instead of static aggregation, TripRank evolves these structural terms via a differential equation until the system converges to a steady-state ranking. We provide a rigorous theoretical proof that TripRank admits a unique steady-state solution under mild damping conditions. Extensive experiments on 3 synthetic and 9 real-world networks demonstrate that TripRank consistently outperforms baseline metrics in both network dismantling and SIR spreading experiments. Furthermore, we reveal an intrinsic exponential scaling law between the optimal competition parameter and the Gini coefficient of triangle distribution, establishing TripRank as a parameter-adaptive framework.