5 papers · 1 filter
Curvature-Distortion Numbers of Graphs: Nonnegative Lin--Lu--Yau Curvature
Qing Xia
We introduce the curvature-distortion number, a scale-invariant parameter measuring the least multiplicative spread of positive edge weights required to make a weighted discrete cu…
Extremal Lin--Lu--Yau Curvature: Graph Density, Girth, and Short Cycles
Qing Xia
We consider the extremal-curvature problem of optimizing a uniform discrete-curvature lower bound over positive edge weights, and develop this problem here for Lin--Lu--Yau curvatu…
Edge-connectivity and LLY curvature of hypergraphs
Qing Xia
Chen, Liu, and You \cite{ChenLiuYou2025} proved that a locally finite connected graph with positive Lin--Lu--Yau curvature has edge-connectivity equal to its minimum degree. Liu an…
Idleness Functions for Ollivier-Ricci Curvature on Hypergraphs
Qing Xia
Let be a locally finite simple hypergraph, equip with the hyperpath metric, and consider the lazy random walk introduced for hypergraph Ollivier--Ricci curva…
Edge-connectivity and non-negative Lin-Lu-Yau curvature
Shiping Liu, Qing Xia
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with…