A novel method for identifying key nodes in multi-layer networks based on dynamic influence range and community importance

Identifying key nodes in multi-layer networks is a hot research topic in complex network science and has broad application prospects, such as in mining enterprises that significantly affecting multi-layer industrial chains. Unlike single-layer networks, nodes in multi-layer networks exhibit heterogeneity due to varying connections and locations. There are also correlations between different network layers, which is particularly evident in industrial chains where companies operate across multiple layers of production, supply and distribution. It is necessary to consider the impact of these layers on the global performance of key node identification. In addition, due to changes in connections, the community structure of each network layer should be different, reflecting the dynamic nature of industrial collaborations and partnerships. However, existing research lacks the model that addresses the above problems. Therefore, this paper proposes a key node identification method based on Dynamic Influence Range and Community Importance (DIRCI), using both local and global information of the multi-layer network simultaneously. DIRCI determines the importance of nodes through three centrality measures: dynamic influence range-based centrality, network layer centrality and community-based centrality. Dynamic influence range-based centrality models node heterogeneity by combining the influence range of nodes and their neighbors with lower computational costs. Network layer centrality captures the corresponding importance for different network layers. Community-based centrality comprehensively considers the importance of community, the importance of each node within the community and between different communities. Experimental results for nineteen multi-layer networks show that DIRCI achieves better performance of key node identification than the latest algorithms.