Work

Ollivier Ricci-flow on weighted graphs

Year: 2024

Type: article

Abstract: : We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by the work of Ni-Lin-Luo-Gao in which the discrete time Ricci flow algorithm has been applied successfully as a discrete geometric approach in detecting communities. Our main result is the existence and uniqueness theorem for solutions to a continuous time normalized Ricci flow. We also display possible solutions to the Ricci flow on path graph and prove the Ricci flow on finite star graph with at least three leaves converges to constant-weighted star.

Source: American Journal of Mathematics

DOI: 10.1353/ajm.2024.a944362

Authors: Shuliang Bai, Yong Lin, Linyuan Lu, Zhiyu Wang, Shing-Tung Yau

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China

Awards: G1738497336, RTG: Mathematical Foundation of Data Science at University of South Carolina

OpenAlex ID: W4404597099

FWCI: 6.107

Cites:

Cited by: 10

Related to: 10