## 1 Introduction  
As science and technology have advanced, it has become clear that numerous natural phenomena can be effectively described using network models [1]. Various systems in the physical world, such as interpersonal relationships on social media [2], protein-protein interactions within biological organisms [3], and even road network [4], can be abstracted as complex networks.  
Identifying key nodes in a network holds significant practical relevance [5]. For instance, in social networks, certain individuals may serve as crucial mediators for information propagation. In transportation networks, specific intersection points can significantly influence the entire network's fluidity. In the context of disease spread research, identifying key propagators can aid in controlling the diffusion of infectious disease [6]. In urban planning, uncovering key nodes within transportation networks can enhance a city's resilience and sustainability [7]. Furthermore, in the realms of social media and Internet advertising, determining key nodes in advertising dissemination can assist in optimizing advertising strategies [8].  
Different types of networks and physical systems necessitate different approaches to determining node importance. A number of traditional algorithms have been proposed by researchers. These classical centrality algorithms have found widespread applications. Over the past few decades, many efficient methods have been developed to assess the nodes' importance by leveraging both local and global information, along with other relevant attributes. For example, EnRenew [9] utilizes local entropy to pinpoint key nodes within networks; Spon [10] assesses node importance using information from neighboring nodes; VoteRank [11] employs a voting mechanism to recognize significant disseminators in networks; and FINDER [12] utilizes reinforcement learning to identify crucial nodes within networks.  
Current investigations into extracting critical information from complex networks have frequently presented researchers with the challenge of reconciling method efficiency with precision [10]. Therefore, based on degree and neighbor node information, this paper introduces an innovative approach to identify crucial nodes within networks, referred to as the degree and neighborhood information centrality (DNC). DNC contends that a node's importance within the network relies on its personal information and the information provided by adjacent nodes. The node's individual information is its degree, while the information from neighboring nodes is determined by the combined local clustering coefficients of its neighbors. The following are the primary advantages of our proposed DNC:  
1. Low time complexity: Since it only utilizes a node's degree and first-order information, DNC only necessitates the computation of first-order neighbor information, leading to a temporal complexity of \(O(|E|)\), allowing DNC to be effectively applied to large-scale networks.
2. High accuracy: DNC surpasses existing baseline methods in terms of accuracy.
3. Parameter setting: DNC can be parameterized to adapt to different networks for optimal performance.  
The sections of this paper that follow are ordered in a logical order. Section 2 includes a synopsis of relevant work, encompassing classical node importance algorithms and recent advancements. Following this, in Section 3, we introduce our baseline methods and proceed with an in-depth presentation of our proposed algorithm, including a demonstration using a small dataset. Section 4 outlines the comprehensive procedure and specifics of our experiments. Finally, we conclude with an overview of the topics covered in this paper.