Network analysis using Forman curvature and Shapley values on hypergraphs

Abstract: In recent years, network models have become more complex with the development of big data. Therefore, more advanced network analysis is required. In this paper, we introduce a new quantitative measure named combinatorial evaluation, which combines the discrete geometry concept of Forman Ricci curvature and the game theory concept of the Shapley value. We elucidated the characteristics of combinatorial evaluation by proving several properties of this indicator. Furthermore, we demonstrated the usefulness of the concept by calculating and comparing the conventional centrality and combinatorial evaluation for a concrete graph. The code is available at https://github.com/Taiki-Yamada-Math/CombinatorialEvaluation.