TL;DR
This paper establishes a Bochner's identity analogue for graphs, introducing a complete tangent graph to relate Ricci curvature to graph structure, bridging concepts from differential geometry and graph theory.
Contribution
It presents a novel Bochner's identity for graphs and introduces the complete tangent graph to connect Ricci curvature with graph properties.
Findings
Derived a Bochner's identity for graphs
Introduced the complete tangent graph concept
Linked Ricci curvature to graph structure
Abstract
We prove an identity on a graph analogous to Bochner's identity on a Riemannian manifold. An auxiliary graph called the complete tangent graph intervenes in the term corresponding to Ricci curvature.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Algebra and Logic · Advanced Topology and Set Theory