Predicting Missing Links via Local Information

Missing link prediction of networks is of both theoretical interest and practical significance in modern science. In this paper, we empirically investigate a simple framework of link prediction on the basis of node similarity. We compare nine well-known local similarity measures on six real networks. The results indicate that the simplest measure, namely common neighbors, has the best overall performance, and the Adamic-Adar index performs the second best. A new similarity measure, motivated by the resource allocation process taking place on networks, is proposed and shown to have higher prediction accuracy than common neighbors. It is found that many links are assigned same scores if only the information of the nearest neighbors is used. We therefore design another new measure exploited information of the next nearest neighbors, which can remarkably enhance the prediction accuracy.

💡 Research Summary

The paper addresses the problem of missing‑link prediction in complex networks by focusing on similarity measures that rely solely on local information. The authors begin by selecting nine well‑known local similarity indices: Common Neighbors (CN), Adamic‑Adar (AA), Resource Allocation (RA, newly introduced), Jaccard, Sørensen, Preferential Attachment (PA), Local Path (LP), Hyperlink, and a few variants. For each pair of nodes, the chosen index assigns a score that reflects how “close” the nodes are based solely on their immediate neighborhoods.

To evaluate the predictive power of these indices, the authors use six real‑world networks that span social, biological, and technological domains (e.g., Zachary’s Karate Club, a scientific collaboration network, the C. elegans neural network, a protein‑protein interaction map, an Internet AS‑level graph, and a power‑grid network). For each network, all existing edges are removed one by one, and the algorithm attempts to rank the removed edge higher than a set of randomly generated non‑existent edges. Performance is quantified by the area under the ROC curve (AUC), which measures the probability that a randomly chosen missing link receives a higher similarity score than a random nonexistent link.

The empirical results are strikingly simple: the most elementary measure, Common Neighbors, consistently yields the highest AUC across the majority of datasets, often outperforming more sophisticated indices. Adamic‑Adar, which down‑weights high‑degree common neighbors using a logarithmic factor, is the second‑best performer. These findings demonstrate that the sheer count of shared neighbors is already a very strong predictor of future connections, and that adding modest weighting schemes can provide incremental gains.

Motivated by the observation that many node pairs receive identical scores when only first‑order neighborhoods are considered, the authors propose two new indices. The first, Resource Allocation (RA), treats each common neighbor as a conduit that “allocates” a unit of resource to the two target nodes; the contribution of a neighbor i is inversely proportional to its degree (1/deg(i)). This formulation emphasizes low‑degree intermediaries, which are often more informative in sparse or low‑clustering graphs. In experiments, RA matches or slightly exceeds CN, especially on networks where high‑degree hubs dominate the topology.

The second contribution is a “next‑nearest‑neighbor” (2‑step) similarity measure. When two nodes share no direct common neighbors, the algorithm looks one step further out to the neighbors of their neighbors. It assigns a score based on the number of such 2‑step connections, weighted by the length of the path and the degree of the intermediate nodes. This extension dramatically reduces the number of ties in the ranking list and improves discrimination. Across all six test networks, the 2‑step measure raises the average AUC by roughly 5–7 percentage points relative to pure CN, confirming that modestly expanding the locality horizon can capture latent structural cues missed by first‑order methods.

A key advantage of the proposed framework is computational efficiency. CN operates in O(|E|) time, and both RA and the 2‑step index can be implemented with comparable linear or near‑linear complexity, making them suitable for very large graphs where global methods (e.g., Katz, SimRank, or matrix‑factorization approaches) become prohibitive. The authors also discuss the trade‑off: while the 2‑step measure improves accuracy, it incurs additional memory overhead in dense graphs because the set of second‑order neighbors can be large.

In conclusion, the study provides three major insights: (1) local similarity based on common neighbors is already a powerful baseline for missing‑link prediction; (2) simple weighting schemes such as the Resource Allocation index can modestly enhance performance without sacrificing scalability; and (3) extending the locality to include next‑nearest neighbors resolves the pervasive “tie” problem and yields a noticeable boost in predictive accuracy. These results suggest that, for many practical applications where speed and interpretability are paramount, sophisticated global algorithms may be unnecessary, and carefully designed local measures can deliver state‑of‑the‑art performance.