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In this paper, we investigate node group significance identification in undirected complex networks by utilizing spectral graph theory of pinning control. Building upon the node significance criterion in network pinning control theory-where important controlled nodes are those maximizing the minimum eigenvalue of the grounded Laplacian matrix after their removal. We propose MFG (Multi-metric Fusion and enhanced Greedy search), a novel key node group identification framework that integrates multi-metric linear fusion and an enhanced greedy search strategy. The methodology initiates by constructing a linear weighted fusion model that synergistically integrates local centrality metrics with global graph properties to pre-screening node groups that are likely to be more important, effectively mitigating the inherent limitations of single-metric evaluation paradigms. Second, a dual search strategy combining second-order neighborhood perturbation and global random walk mechanisms is developed to optimize the myopic nature of conventional greedy algorithms. Through iterative selection within pre-screened node groups, this approach identifies nodes maximizing the minimum eigenvalue of the grounded Laplacian matrix, achieving an optimal balance between local optimization and global search capabilities. Third, computational efficiency is enhanced using a modified inverse power method for eigenvalue calculation, reducing the complexity of traditional spectral computations. Comprehensive simulations on generated networks and real-world networks demonstrate the framework’s superiority. The evaluation of the proposed algorithm incorporates three aspects: 1) comparison of the minimum eigenvalues under different algorithms; 2) SIR epidemic modeling for propagation capability assessment; 3) topological analysis of identified key nodes. Simulation results reveal two significant findings: a) Our method outperforms state-of-the-art benchmarks(NPE,AGM,HVGC) in maximizing the grounded Laplacian’s minimum eigenvalue across synthetic(NW small-world,ER) and real-world networks,particularly at critical control sizes; b) The identified critical node groups exhibit distinctive topological signatures-typically combining high-degree hubs with strategically located bridges-that optimally balance local influence and global connectivity. Critically, SIR propagation modeling confirms these topologically optimized groups accelerate early-stage outbreaks and maximize global saturation coverage,directly linking structural signatures to superior dynamic influence. These findings provide guidelines for information propagation control in social networks.
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Keywords:
- Complex network /
- Node group importance /
- Pre-screening algorithm /
- Spectral graph theory of the grounded Laplacian matrix
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