TL;DR
Experimental results in seven complex networks of the real world show that the proposed hybrid centrality called k-core neighborhood density (KND) remarkably balances rank distribution and accuracy, and the identified influential nodes have a superior ability to spread their influence over a wide area of a network.
This study introduces a new ranking framework that integrates a quasi-Laplacian structural measure with a gravity-inspired aggregation process and demonstrates that the proposed framework consistently outperforms existing techniques in terms of accuracy, resolution, and computational simplicity.
Identifying influential nodes in complex networks is a fundamental problem with applications in information diffusion, epidemic control, infrastructure robustness, and biological systems. Traditional approaches rely on structural centrality measures, such as degree, betweenness, closeness, and PageRank, which quantify node importance based on network connectivity. However, these measures do not explicitly account for diffusion dynamics and the structural impact of node removal, where both spreading capability and network resilience play a critical role. In this paper, we propose a unified framework that jointly captures diffusion-based influence and structural resilience. We first introduce an SIR-based centrality in which node influence is defined by its spreading capability, while resilience is quantified by measuring the change in total network diffusion after node removal. To address the computational cost of this formulation, we propose the Resilient-Influential Node (RIN) centrality, which efficiently approximates the unified objective by combining classical centrality measures with a Laplacian-based structural adjustment. Experimental results on multiple real-world networks, using SIR-based rankings as ground truth, show that the proposed RIN framework provides a consistent and principled characterization of influential and resilient nodes across diverse network structures.
WKDH fuses local structural attributes with global structural attributes via a multiplicative weighted synergy model, simultaneously capturing local connection “quantity,” local connection “quality,” and global core-layer position, and achieves linear computational complexity of O(m).
Spectral Efficiency Centrality (SEC), a temporal spectral centrality framework that quantifies node importance by evaluating the change in spectral radius caused by node removal across temporal snapshots, and ASEC, an efficient approximation based on Perron-Frobenius theory and first-order eigenvalue perturbation that offers a computationally efficient solution for large-scale temporal networks.
A novel heuristic community detection algorithm, termed CoDeSEG, which identifies communities by minimizing the network's two-dimensional structural entropy within a potential game framework, and introduces a structural entropy-based node overlapping heuristic for detecting overlapping communities, with a near-linear time complexity.