Ollivier Ricci Curvature of Directed Hypergraphs

07/10/2019
by   Marzieh Eidi, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/22/2018

Curvature of Hypergraphs via Multi-Marginal Optimal Transport

We introduce a novel definition of curvature for hypergraphs, a natural ...
research
10/14/2019

A Simple Differential Geometry for Networks and its Generalizations

Based on two classical notions of curvature for curves in general metric...
research
11/19/2018

Forman-Ricci Curvature for Hypergraphs

In contrast to graph-based models for complex networks, hypergraphs are ...
research
10/21/2022

Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework

Bridging geometry and topology, curvature is a powerful and expressive i...
research
10/17/2018

Forman's Ricci curvature - From networks to hypernetworks

Networks and their higher order generalizations, such as hypernetworks o...
research
02/16/2021

About Weighted Random Sampling in Preferential Attachment Models

The Barabási-Albert model is a popular scheme for creating scale-free gr...
research
06/03/2021

Combinatorial Conditions for Directed Collapsing

The purpose of this article is to study directed collapsibility of direc...

Please sign up or login with your details

Forgot password? Click here to reset