5 papers · 1 filter
Finding core subgraphs of directed graphs via discrete Ricci curvature flow
Juan Zhao, Jicheng Ma, Yunyan Yang +1
Ricci curvature and its associated flow offer powerful geometric methods for analyzing complex networks. While existing research heavily focuses on applications for undirected grap…
Core detection via Ricci curvature flows on weighted graphs
Juan Zhao, Jicheng Ma, Yunyan Yang +1
Graph Ricci curvature is crucial as it geometrically quantifies network structure. It pinpoints bottlenecks via negative curvature, identifies cohesive communities with positive cu…
Lin-Lu-Yau Ricci curvature on hypergraphs
Yulu Tian, Liang Zhao
In this paper, we introduce a unified framework for defining Lin-Lu-Yau (LLY) Ricci curvature on both undirected and directed hypergraphs. By establishing upper bounds and monotoni…
Community detection of hypergraphs by Ricci flow
Yulu Tian, Jicheng Ma, Yunyan Yang +1
Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricc…
Nonlinear Diffusion Equations on Graphs: Global Well-Posedness, Blow-Up Analysis and Applications
Mengqiu Shao, Yunyan Yang, Liang Zhao
For a nonlinear diffusion equation on graphs whose nonlinearity violates the Lipschitz condition, we prove short-time solution existence and characterize global well-posedness by e…