  Curvature serves as a potent and descriptive invariant, with its efficacy
validated both theoretically and practically within graph theory. We employ a
definition of generalized Ricci curvature proposed by Ollivier, which Lin and
Yau later adapted to graph theory, known as Ollivier-Ricci curvature (ORC). ORC
measures curvature using the Wasserstein distance, thereby integrating
geometric concepts with probability theory and optimal transport. Jost and Liu
previously discussed the lower bound of ORC by showing the upper bound of the
Wasserstein distance. We extend the applicability of these bounds to discrete
spaces with metrics on integers, specifically hypergraphs. Compared to prior
work on ORC in hypergraphs by Coupette, Dalleiger, and Rieck, which faced
computational challenges, our method introduces a simplified approach with
linear computational complexity, making it particularly suitable for analyzing
large-scale networks. Through extensive simulations and application to
synthetic and real-world datasets, we demonstrate the significant improvements
our method offers in evaluating ORC.
