A condition for non-negative Lin-Lu-Yau curvature

TL;DR

This paper establishes a lower bound on the minimum vertex degree of locally finite graphs that guarantees non-negative Lin-Lu-Yau curvature, contributing to understanding curvature conditions in graph theory.

Contribution

It provides a specific degree threshold ensuring non-negative Lin-Lu-Yau curvature and analyzes the bound's sharpness, advancing curvature analysis in graphs.

Findings

Derived a lower bound on vertex degree for non-negative curvature

Proved the bound's sharpness in certain graph classes

Enhanced understanding of Ollivier-Ricci curvature in graphs

Abstract

We investigate the Ollivier-Ricci curvature and its modification introduced by Lin, Lu, and Yau on locally finite graphs. The main contribution of this work is a lower bound on the minimum vertex degree of a graph ensuring non-negative Lin-Lu-Yau curvature. Additionally, we examine the sharpness of this lower bound.