A construction of graphs with positive Ricci curvature

TL;DR

This paper investigates how connecting two complete graphs with edges affects the Ricci curvature of the resulting graph, providing calculations and conditions for achieving positive Ricci curvature.

Contribution

It introduces the concept of gluing graphs and determines the minimum number of edges needed to ensure positive Ricci curvature on the combined graph.

Findings

Ricci curvature increases with more added edges

Explicit calculation of Ricci curvature for each edge

Minimum edges required for positive Ricci curvature

Abstract

Two complete graphs are connected by adding some edges. The obtained graph is called the gluing graph. The more we add edges, the larger the Ricci curvature on it becomes. We calculate the Ricci curvature of each edge on the gluing graph and obtain the least number of edges that result in the gluing graph having positive Ricci curvature.