One key challenge within the domain of network science is accurately finding important nodes within a network. In recent years, researchers have proposed various node centrality indicators from different perspectives. However, many existing methods have their limitations. For instance, certain approaches lack a balance between time efficiency and accuracy, while the majority of research neglects the significance of local clustering coefficients, a crucial node property. Thus, this paper introduces a centrality metric called DNC (degree and neighborhood information centrality) that considers both node degree and local clustering coefficients. The combination of these two aspects provides DNC with the ability to create a more comprehensive measure of nodes’ local centrality. In addition, in order to obtain better performance in different networks, this paper sets a tunable parameter $\alpha$ to control the effect of neighbor information on the importance of nodes. Subsequently, the paper proceeds with a sequence of experiments, including connectivity tests, to validate the efficacy of DNC. The results of the experiments demonstrate that DNC captures more information and outperforms the other eight centrality metrics.

Identifying critical edges in complex networks is a fundamental challenge in the study of complex networks. Traditional approaches tend to rely solely on either global information or local information. However, this dependence on a single information source fails to capture the multi-layered complexity of critical edges, often resulting in incomplete or inaccurate identification. Therefore, it is essential to develop a method that integrates multiple sources of information to enhance critical edge identification and provide a deeper understanding and optimization of the structure and function of complex networks. In this paper, we introduce a Global–Local Hybrid Centrality method which integrates a second-order neighborhood index, a first-order neighborhood index, and an edge betweenness index, thus combining both local and global perspectives. We further employ the edge percolation process to evaluate the significance of edges in maintaining network connectivity. Experimental results on various real-world complex network datasets demonstrate that the proposed method significantly improves the accuracy of critical edge identification, providing theoretical and methodological support for the analysis and optimization of complex networks.