Extending Graph-Based LP Techniques for Enhanced Insights Into Complex Hypergraph Networks

Many real-world problems can be modelled in the form of complex networks. Social networks such as research collaboration networks and facebook, biological neural networks such as human brains, biomedical networks such as drug-target interactions and protein-protein interactions, technological networks such as telephone networks, transportation networks and power grids are a few examples of complex networks. Any complex system with entities and interactions existing between the entities can be modelled as a graph mathematically, with nodes representing entities and edges reflecting interactions. In numerous real-world circumstances, interactions are not confined to pair of entities. Majority of these intricate systems inherently possess hypergraph structures, characterized by interactions that extend beyond pairwise connections. Existing studies often transform complex interactions at a higher level into pairwise interactions and subsequently analyze them. This conversion frequently leads to both the loss of information and the inability to reconstruct the original hypergraph from the transformed network with pairwise interactions. One of the most essential tasks that can be performed on these graphs is Link Prediction (LP), which is the task of predicting future edges (links) in a graph. LP in graphs is well investigated. This article presents a novel methodology for predicting links in hypergraphs. Unlike conventional approaches that transform hypergraphs into graphs with pairwise interactions, the proposed method directly leverages the inherent structure of hypergraphs in predicting future interaction between a pair of nodes. This is motivated by the fact that hypergraphs enable the depiction of intricate higher-order relationships through hyperlinks, enhancing their representation. Their capacity to capture complex structural patterns improves predictive capabilities. Node neighborhoods within hypergraphs offer a comprehensive framework for LP, where hyperlinks simplify interactions between nodes across cliques. We propose a novel method of Link Prediction in Hypergraphs (LPH) to predict interactions within hypergraphs, maintaining their original structure without conversion to graphs, thus preserving information integrity. The proposed approach LPH extends local similarity measures like Common Neighbors, Jaccard Coefficient, Adamic Adar, and Resource Allocation, along with a global measure, Katz index, to hypergraphs. LPH’s effectiveness is assessed on six benchmark hyper-networks, employing evaluation metrics such as Area under ROC curve, Precision, and F1-score. The proposed measures of LP on hypergraphs resulted in an average enhancement of 10% in terms of Area under ROC curve compared to contemporary as well as conventional measures. Additionally, there is an average improvement of 70% in precision and around 50% in F1-score. This methodology presents a promising avenue for predicting pairwise interactions within hypergraphs while retaining their inherent structural complexity as well as information integrity.