Network analysis using Forman curvature and Shapley values on hypergraphs

TL;DR

This paper introduces a novel combinatorial evaluation measure for network analysis that combines Forman Ricci curvature and Shapley values, demonstrating its properties and usefulness on a concrete graph.

Contribution

It proposes a new quantitative measure called combinatorial evaluation, integrating discrete geometry and game theory for advanced network analysis.

Findings

The measure has well-defined properties.

It effectively compares with traditional centrality measures.

Code implementation is publicly available.

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.