## 2 Related Work  
At present, many researchers in the field of complex networks focus on the mining of important nodes in networks; that is, ranking the importance of all nodes in a network as a whole. Existing research has primarily aimed to develop an identification algorithm for influential nodes. Inspired by the heuristic scheme, [PERSON] et al. [17] proposed the price-performance-ratio PPRank method, selecting nodes in a given range and aiming to improve the performance of the diffusion. [PERSON] et al. [18] proposed a method of ranking node importance based on multi-criteria decision-making (MCDM). The weight of each criterion is calculated by an entropy weighting method, which overcomes the impact of the subjective factor. [PERSON] et al. [19] proposed a method of calculating the importance degree of urban rail transit network nodes based on h-index, which considers the topology, passenger volume, and passenger flow correlation of the urban rail network. [PERSON] et al. [20] proposed a relationship matrix resolving model to identify vital nodes based on community (IVNC), as an attempt to identify influential nodes in OSNs.  
However, the study on node mining based on relative importance remains limited. The earliest study on relative importance in networks is that on a personalized variant HITS algorithm [21]. [PERSON] [22] and [PERSON] et al. [23] later proposed their own variant PageRank algorithms, which consider the relative importance of nodes in a network. [PERSON] et al. [24] defined the universal framework of mining algorithms for relatively important nodes and proposed that the relative importance of nodes in a network relates to one node set or one group of specified node sets. [PERSON] et al. [25] proposed a path probabilistic summation method, which defines the importance of any node relative to the nearest neighbor node as the probability of jumping from the node to the nearest neighbor node in the random walk process. [PERSON] et al. [26] proposed a cluster particle propagation method, which is used to evaluate the relative importance of nodes. [PERSON] et al. [27] used shortest distance as a measurement indicator of relative importance. [PERSON] et al. [28] used the reciprocal of the \(P\) norm of the shortest distance as a measurement indicator of relative importance. In addition, some researchers have considered mining deep network information by using network embedded learning methods [29; 30; 31; 32; 33; 34; 35]. For example, some classical network-embedded learning algorithms have been used to mine relatively important nodes in networks.  
Although some algorithms have been employed to mine relatively important nodes in networks, they suffer from problems that require immediate resolution, such as low accuracy and narrow use range. Therefore, novel and efficient methods for mining relatively important nodes need to be developed.  
In the study of complex networks, the most classic and most widely used relative importance calculation indicators include the Ksmar index [11], PPR index [21], and Katz index [36]. [PERSON] et al. [37] proposed a relatively important node mining algorithm based on neighbor layer diffuse (NLD) in 2021, which is the latest relatively important node algorithm. In Section 4, we empirically compare our method with these methods using various real world networks.