## 2 Related Works  
In the past few years, critical nodes in complex networks have received special attention from researchers. We present a quick review of current algorithms in this section.  
Researchers have presented a variety of classical centrality measurements based on diverse concepts and ideas. Degree centrality [13] quantifies the number of neighbors a node has. Although degree centrality calculations are straightforward, they frequently overlook the overall structure of complex networks, resulting in diminished accuracy. Eigenvector centrality [14] computes a node's score by considering the centrality of its neighbors. Closeness centrality [15] evaluates the average distance from the present node to all other nodes along the shortest paths. Betweenness centrality [13] measures a node's significance by allying shortest paths that traverse through it, reflecting its significance as a bridge node. The VoteRank algorithm [11] employs a voting mechanism to assign scores to nodes.  
The fundamental concept behind the K-Shell algorithm involves identifying core nodes within a network by iteratively eliminating nodes with the lowest degrees [16]. Yet, the K-Shell algorithm grapples with several limitations; it predominantly focuses on node degrees, disregards other pertinent network attributes, and is unable to differentiate the score of nodes within the same layer. Based on the K-Shell concept, [PERSON] et al. [17] suggested a customized hierarchical method, augmenting it with more topological information. [PERSON] et al. [18] proposed an enhanced K-Shell algorithm that identifies important nodes from higher-level K-Shells to lower-level K-Shells using node information entropy. A mixed-degree decomposition approach was developed by [PERSON] et al. [19]. This method integrates the concept of depletion degree to assess the impact of eliminated nodes on a specific node, as well as remaining degree to assess the impact of remaining nodes on that specific node.  
Furthermore, methods for identifying important nodes based on improved gravity models have also gained significant attention [20; 21; 22; 23; 24]. Inspired by the gravity model, node degrees are considered as masses, and the distance is represented by the shortest path between two nodes. The importance score of nodes is then calculated using the formula for universal gravitation [20]. However, in practical usage, the gravity model is associated with high time complexity, and using node degree as mass often lacks accuracy due to the limited information node degrees represent [21]. [PERSON] et al. introduced weighted gravity centrality [22], which combines eigenvector centrality with the gravity model, integrating global and local information. [PERSON] et al. introduced KSGC, which added an attraction coefficient to the K-Shell-based generalized gravity model [21]. [PERSON] et al. proposed MCGM [23], considering more node information and combining node degree, K-Shell, and EC as node masses. Recently, [PERSON] et al. proposed a novel communication-based adaptive gravity model, CAGM, an innovative communication-based adaptive gravity model that assesses each node's score by using the likelihood and intensity of influence from nearby nodes within its impact radius [24].  
Researchers have also been devoted to using deep learning to identify important nodes in complex networks [12; 25; 26]. [PERSON] et al. proposed employing graph convolutional networks to locate key nodes [25]. Using graph convolutional networks, [PERSON] et al. [26] developed a method for finding critical nodes while accounting for different levels of network structural features. [PERSON] et al. introduced FINDER, a strategy based on reinforcement learning for finding key nodes [12].