# A Key Node Mining Method Based on K-Shell and Neighborhood Information
## 1 Introduction
However, they may not be very suitable for large-scale networks due to their intricate computations and high time costs [21]. The K-shell (KS), proposed by [PERSON] et al., can quickly rank the importance of nodes in a network and is suitable for large-scale networks [26]. This method categorizes nodes based on their degrees, thus identifying whether a node serves as a core within the network. While this approach heralds a novel measurement paradigm, it introduces a significant issue of monotonicity, whereby it fails to discern variations in node importance within the same stratum. To address this, researchers have proposed a series of improved methods, such as extended coreness centrality (CNC+) [27], classified neighbors (CN) [28], KSIF [29], and mixed degree decomposition (MDD) [30], among others. Traditional methods for mining important nodes often rely on the degree as the core criterion for assessing node importance. While this intuitive approach is effective and yields significant results, the degree alone does not fully capture a node's importance. Nodes with a low degree can also play crucial roles in the network. For example, bridge nodes that connect different communities may have a small degree, but they have a high level of influence and are undeniably important. Additionally, the clustering coefficient, another vital attribute of a node, is seldom utilized in existing methods for mining important nodes [31]. Therefore, this paper introduces an innovative method for identifying key nodes in the network based on K-shell and node neighborhood information, called KCH. KCH posits that the importance of a node in the network is determined by both the node's own information and the node's neighborhood information. The individual information of a node is represented by the KS value, while the neighborhood information of a node is determined by the combined local clustering coefficient and structural hole coefficient of its adjacent nodes. The time complexity of the KCH method is \(O(\overline{n}\cdot|E|)\), where \(\overline{n}\) is the average degree of the network, and \(|E|\) is the number of edges in the network. Below are the main advantages of our proposed KCH:  
1. KCH adopts a hybrid approach to integrating both global and local information. The KCH method enhances the traditional K-shell approach by incorporating comprehensive network information. It combines structural hole data and the local clustering coefficient--an essential node attribute--with local topological structure information. 2. The experimental results on connectivity, monotonicity, and null models across ten networks demonstrate that KCH outperforms other K-shell variant methods and non-K-shell variant methods such as collective influence (CI), SC, hierarchical K-shell (HKS). The KCH shows superior accuracy, monotonicity, and universality, effectively identifying the influence of a node within the network. The remainder of this paper is organized as follows: Section 2 of the paper reviews related work on important node mining. Section 3 introduces the baseline methods and the specific details of the KCH method proposed in this paper. Section 4 describes the experiments conducted to evaluate the performance of KCH, analyzes the experimental results, and assesses the effectiveness of the KCH method. Finally, Section 5 summarizes the key findings of the paper.