10 papers
CurvFlow-DTA: dual-graph discrete Ricci curvature flow for drug--target affinity prediction
Jicheng Ma, Yunyan Yang, Juan Zhao +1
Graph neural networks are widely used for drug--target affinity (DTA) prediction, and discrete Ricci curvature has recently been used to characterize molecular graph geometry. Exis…
Evolving edge weights via local entropy flow and cohesion flow on graphs
Juan Zhao, Jicheng Ma, Yunyan Yang +1
In this paper, we first propose two different quantities on graphs, namely local entropy and cohesion, then design two corresponding flows for edge weights: the local entropy flow…
An Efficient Entropy Flow on Weighted Graphs: Theory and Applications
Juan Zhao, Jicheng Ma, Yunyan Yang +1
We propose a novel entropy flow on weighted graphs, which provides a principled framework that characterizes the evolution of probability distributions over graph structures while…
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…
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…