# Ollivier Ricci Curvature of Directed Hypergraphs

## TL;DR

This paper introduces a new way to measure Ricci curvature on directed hypergraphs, extending Ollivier's graph curvature concept through an optimal transport framework between vertex sets.

## Contribution

It generalizes Ollivier Ricci curvature to directed hypergraphs using a novel optimal transport-based definition.

## Key findings

- Provides a new curvature measure for directed hypergraphs
- Extends Ollivier's graph curvature to more complex structures
- Lays groundwork for analyzing geometric properties of hypergraphs

## Abstract

We develop a definition of Ricci curvature on directed hypergraphs and explore the consequences of that definition. The definition generalizes Ollivier's definition for graphs. It involves a carefully designed optimal transport problem between sets of vertices.