4 papers · 1 filter
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…
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…
A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph
Yulu Tian, Liang Zhao
In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to…
Calculus of variations on hypergraphs
Mengqiu Shao, Yulu Tian, Liang Zhao
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function…