Centrality with Entropy in Hypergraphs Based on Similarity Measures

Abstract

Hypergraphs and simplicial complexes can be used to model higher-order interactions. Graphs are limited to model and describe pairwise interactions. In this study, the issue of centrality in hypergraphs was studied. We introduce centrality measures based on the entropy of nodes and hyperedges in the hypergraphs. Until now, a lot of measures from various perspectives have been proposed to identify influential nodes, yet non provides a complete solution to the centrality problem. Because there are different perspectives on centrality. It is important to try different models to reach a solution in centrality problems. Entropy, which is a measure of uncertainty, is a guide in centrality measurements. It can produce ideal solutions for centrality. In complex systems, the entropy can be measured by different methods. In this study, the entropy calculation was made according to the union, intersection, and jaccard similarity values for nodes. The way that similarity is measured indicates the type of centrality. Local centralities were detected more precisely when the degree and union similarity values were used. The intersection and jaccard similarities showed us the global centralities. Traditional methods of centrality were also compared with the results of the proposed method. The accuracy of the method was tested with different hypergraph datasets. It has been shown that we can produce efficient results with different similarity parameters according to our wishes in hypergraphs.