# A Key Node Mining Method Based on K-Shell and Neighborhood Information
## 2 Related Works
### Local Indices  
Local index-based centrality methods often assess the node's importance by collecting information from the node's neighborhood. Examples include DC, H-index, and SC. DC is centered around the degree, positing that a node's importance increases with the number of its neighbors [19]. Although this algorithm is simple, it has a fatal flaw: it only considers the number of adjacent nodes and ignores edge weights, which restricts its performance in weighted networks. The H-index, extended to complex networks by [PERSON] and colleagues, measures a node's importance through the degree of its neighbors [22]. SC, proposed by [PERSON] et al., evaluates the importance of a node by the sum of the node's degree and the degrees of its neighbors [20].  
Focusing solely on a node and its first-order neighbors often lacks precision and has significant limitations. Therefore, methods that consider a node's local information without being restricted to the nearest neighbors have been widely proposed. Such methods are referred to as semi-local index-based centrality methods; for example, SLC, local structural centrality (LSC), ERM, and Spon. SLC, proposed by [PERSON] et al., follows a rationale similar to SC, measuring the importance of a node by the sum of the degrees of the node and its neighbors [21]. However, SLC fully utilizes the information of the node's higher-order neighbors, whereas SC only uses the degree information of the first-order neighbors. [PERSON] et al. proposed Spon, which measures the importance of a node by calculating the \"neighbor ratio\" of a node's neighbors. The \"neighbor ratio\" refers to the ratio of the number of a node's first-order to its second-order neighbors, essentially still using the degree to measure the importance of a node [33]. Unlike the aforementioned methods that rely solely on degree, [PERSON] et al. proposed LSC, which takes into account both the degree of a node and its topological information [34]; [PERSON] et al. proposed ERM, incorporating the concept of entropy from information theory into node centrality, assessing the importance of a node based on the information entropy of the node and its first-order and second-order neighbors [23].  
Most of the aforementioned methods are degree-based, but a node's degree is not necessarily indicative of its importance [27]. The term \"structural hole\" originates from social network research [35]. In networks, structural hole nodes serve as bridges or connectors between different communities within the network. Monitoring structural hole nodes can effectively curb the spread of rumors, and these nodes have advantages in information dissemination, innovation, and resource integration [36; 37]. If structural hole nodes are removed, different communities within the network become disconnected; thus, structural hole nodes often have a low degree but possess significant importance.  
Local index-based centrality methods only utilize the local neighborhood information of a node (i.e., information between the node and its neighbors) to rank the importance of the node. These methods are advantageous due to their computational simplicity and high efficiency, making them suitable for large- and medium-sized networks. However, they struggle to assess node importance from a holistic perspective and find it difficult to measure the true importance of nodes such as structural holes.