## 1 Introduction  
With the vigorous growth of network and information technology represented by the Internet, human society has entered a new and complex era of networks. Information mining in complex networks is important in theoretical research and offers great application and socioeconomic values [1; 2; 3; 4]. For example, if users can unearth important nodes or edges in the spread network of a virus, then they can curb the spread of the virus in a short time by isolating or cutting off the important nodes or edges in the virus network at the beginning of the virus spread and thereby eliminate unnecessary economic losses [5]. Efficient information mining in complex networks has naturally become a key topic that continues to attract the attention of many scholars. The existing studies on complex network information mining are generally ranked on the basis of the importance of all nodes and edges in the network [6; 7; 8; 9; 10]. However, determining which nodes are the most important in the network relative to one or one group of specific nodes presents an issue. This problem reminds us about the practical significance of mining relatively important information in networks, especially very large-scale ones. The relative importance of nodes refers to the importance of nodes relative to known important nodes. It is also called proximity or similarity [11]. According to the key idea of relative importance, information mining in a complex network can be described as a process in which the importance of a node in a network relative to a known important node is quantified and the importance of a node relative to a known important node set is calculated to identify the relatively important nodes in the network. The central idea of relative importance can be widely used in many fields. For example, potential criminals can be found using known criminal data in the field of criminal networks, and terrorists in hiding can be captured on the basis of known terrorist data [12; 13]. In the bionetwork field, people susceptible to diseases can be identified for timely treatment and isolation on the basis of relevant information on populations infected with known infectious diseases. Unknown pathogenic genes may be determined according to known pathogenic gene information in protein networks [14]. In the field of power grids, on the premise that the information on important power generation units or circuit breakers is known, finding relatively important power generation units, circuit breakers, etc. is prioritized for protection, in order to effectively avoid large-area power outages caused by successive faults. Mining relatively important nodes in complex networks obviously offers great research significance and application value [15]. The node distance distribution in a complex network quantifies many types of topological information in the network, including the degree of nodes, average degree of the network, diameter of the network, closeness centrality of nodes, and average path length of the network [16]. Therefore, the study on the relative importance of nodes in a network based on node distance distribution in the network will contribute to the accurate mining of relatively important nodes in networks. In the current study, the distance distribution of all nodes in a network is calculated. On the basis of known important node information, the differences in distance distribution between known important nodes and target nodes are measured from three dimensions, namely, direction, distance, and distribution. A relatively important node mining method based on distance distribution and multi-index fusion (DDMF) is proposed. The DDMF method involves two main steps: First, the distance distribution of all nodes (including known important nodes and target nodes) is calculated on the basis of the shortest distance between nodes in the network. Then, the calculated results are converted into vector form. Second, multi-index fusion is made for cosine similarity, Euclidean distance, and relative entropy.