Hierarchical influential node identification in multi-agent networks based on triangular recursive compression

The identification of influential nodes in complex networks is a core research topic in the field of network science. Existing methods often rely on the topological features of static networks, which struggle to fully capture the characteristics of nodes in dynamic networks. To address this issue, this paper proposes a hierarchical control node selection algorithm based on triangular recursive compression and control influence index (HTRCI) to identify influential nodes and enhance network stability accurately. Firstly, the control influence index is introduced, integrating multiple attributes such as node energy level and neighbor variation rate to evaluate node importance comprehensively. Additionally, an efficient triangle detection algorithm based on intersection matrices is designed to improve the extraction efficiency of triangular features. To address the influence overlap caused by shared nodes and edges within triangular structures, this paper proposes a triangle control node selection method incorporating a conflict resolution mechanism. In non-triangular regions, this paper designs a non-triangular structure control node identification algorithm based on coverage maximization, which regulates the distribution of control nodes by introducing a repulsion mechanism. Furthermore, a hierarchical control node selection strategy is proposed to iteratively compress the management regions of control nodes, reducing the number of control nodes and improving the global control efficiency of the network. In NS3 simulations, the proposed algorithm is evaluated on six real-world networks and compared with eight state-of-the-art algorithms. The results demonstrate that the HTRCI algorithm exhibits significant advantages in terms of information transmission rate and network stability, validating its superiority and applicability in complex dynamic networks.