Love tHy Neighbour: Remeasuring Local Structural Node Similarity in Hypergraph-Derived Networks

Abstract: The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and hence, extensions thereof viz. hypergraphs are used instead. Measuring proximity between node pairs in such a setting calls for a revision in the topological measures of similarity, lest the hypergraph structure remains under-exploited. We, in this work, propose a multitude of hypergraph-oriented similarity scores between node-pairs, thereby providing novel solutions to the link prediction problem. As a part of our proposition, we provide theoretical formulations to extend graph-topology based scores to hypergraphs. We compare our scores with graph-based scores (over clique-expansions of hypergraphs into graphs) from the state-of-the-art. Using a combination of the existing graph-based and the proposed hypergraph-based similarity scores as features for a classifier predicts links much better than using the former solely. Experiments on several real-world datasets and both quantitative as well as qualitative analyses on the same exhibit the superiority of the proposed similarity scores over the existing ones.