Link prediction aims to predict the potential existence of links between two unconnected nodes within a network based on the known topological characteristics. Evaluation metrics are used to assess the effectiveness of algorithms in link prediction. The discriminating ability of these evaluation metrics is vitally important for accurately evaluating link prediction algorithms. In this study, we propose an artificial network model, based on which one can adjust a single parameter to monotonically and continuously turn the prediction accuracy of the specifically designed link prediction algorithm. Building upon this foundation, we show a framework to depict the effectiveness of evaluating metrics by focusing on their discriminating ability. Specifically, a quantitative comparison in the abilities of correctly discerning varying prediction accuracies was conducted encompassing nine evaluation metrics: Precision, Recall, F1-Measure, Matthews correlation coefficient, balanced precision, the area under the receiver operating characteristic curve (AUC), the area under the precision-recall curve (AUPR), normalized discounted cumulative gain (NDCG), and the area under the magnified receiver operating characteristic. The results indicate that the discriminating abilities of the three metrics, AUC, AUPR, and NDCG, are significantly higher than those of other metrics.

Identifying key spreaders in a network is one of the fundamental problems in the field of complex network research, and accurately identifying influential propagators in a network holds significant practical implications. In recent years, numerous effective methods have been proposed and widely applied. However, many of these methods still have certain limitations. For instance, some methods rely solely on the global position information of nodes to assess their propagation influence, disregarding local node information. Additionally, certain methods do not consider clustering coefficients, which are essential attributes of nodes. Inspired by the quality formula, this paper introduces a method called Structural Neighborhood Centrality (SNC) that takes into account the neighborhood information of nodes. SNC measures the propagation power of nodes based on first and second-order neighborhood degrees, local clustering coefficients, structural hole constraints, and other information, resulting in higher accuracy. A series of pertinent experiments conducted on 12 real-world datasets demonstrate that, in terms of accuracy, SNC outperforms methods like CycleRatio and KSGC. Additionally, SNC demonstrates heightened monotonicity, enabling it to distinguish subtle differences between nodes. Furthermore, when it comes to identifying the most influential Top-k nodes, SNC also displays superior capabilities compared to the aforementioned methods. Finally, we conduct a detailed analysis of SNC and discuss its advantages and limitations.

Link prediction aims to identify unknown or missing connections in a network. The methods based on network structure similarity, known for their simplicity and effectiveness, have garnered widespread attention. A core metric in these methods is “proximity”, which measures the similarity or linking probability between two nodes. These methods generally operate under the assumption that node pairs with higher proximity are more likely to form new connections. However, the accuracy of existing node proximity-based link prediction algorithms requires improvement. To address this, this paper introduces a Link Prediction Algorithm Based on Weighted Local and Global Closeness (LGC). This algorithm integrates the clustering coefficient to enhance prediction accuracy. A significant advantage of LGC is its dual consideration of a network’s local and global features, allowing for a more precise assessment of node similarity. In experiments conducted on ten real-world datasets, the proposed LGC algorithm outperformed eight traditional link prediction methods, showing notable improvements in key evaluation metrics, namely precision and AUC.

In research on complex networks, mining relatively important nodes is a challenging and practical work. However, little research has been done on mining relatively important nodes in complex networks, and the existing relatively important node mining algorithms cannot take into account the indicators of both precision and applicability. Aiming at the scarcity of relatively important node mining algorithms and the limitations of existing algorithms, this paper proposes a relatively important node mining method based on distance distribution and multi-index fusion (DDMF). First, the distance distribution of each node is generated according to the shortest path between nodes in the network; then, the cosine similarity, Euclidean distance and relative entropy are fused, and the entropy weight method is used to calculate the weights of different indexes; Finally, by calculating the relative importance score of nodes in the network, the relatively important nodes are mined. Through verification and analysis on real network datasets in different fields, the results show that the DDMF method outperforms other relatively important node mining algorithms in precision, recall, and AUC value.