Identifying Potential Critical Nodes of Complex Networks via Quantifying Hierarchical Local Propagation Capabilities

Complex networks show substantial heterogeneity in node connectivity, resulting in a few nodes that play critical roles in enhancing the system robustness. Existing node centrality measures often struggle to balance the accuracy and computational efficiency. We propose HLPRank, a novel hybrid centrality algorithm that integrates the global hierarchical structure with local neighborhood propagation capability to identify key nodes. Experimental results demonstrate that HLPRank inflicts effectively persistent damage to network topologies, such as the largest connected component (LCC) and average remaining edges (AREs), with fewer than 40% and 11% of targeted attacks, respectively, compared with the average attack ratios in benchmark algorithms. It can also significantly decrease information propagation efficiency, achieving an advantageous balance between rapid dismantling and damage severity. The information blocking experiment conducted employing the susceptible-infectious-recovered (SIR) model reveals that HLPRank can preferentially immunize subsets of dominant nodes, partitioning information domains, and efficiently blocking transmission. HLPRank captures nodes' propagation capabilities within hierarchical local neighborhoods, highlighting bridging nodes' importance in network vulnerability, providing new insights for enhancing system resilience and information control.