Entropy flow on weighted graphs provides a rigorous, convergent framework for evolving distributions on graphs and achieves community detection accuracy comparable to Ricci flow at a small fraction of the computational cost.
On the ricci flow on trees
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
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A discrete Ricci flow on graphs converges exponentially to prescribed Lin-Lu-Yau curvatures iff attainable, with an explicit max-edge-density condition for constant curvature on girth-at-least-6 graphs.
Classification of finite trees with positive-curvature discrete Einstein metrics via λ_max(R_T)<0, giving explicit endpoint families for long-spine caterpillars and exhaustive algebraic verification for short spines.
The Calabi flow on finite graphs converges globally if and only if a weight function exists realizing the prescribed curvature, with convergence for constant curvature under topological conditions.
Existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature is established via Perron-Frobenius theory, with positive curvature possible only on caterpillar trees and edge weights decreasing radially from the maximal edge.
citing papers explorer
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An Efficient Entropy Flow on Weighted Graphs: Theory and Applications
Entropy flow on weighted graphs provides a rigorous, convergent framework for evolving distributions on graphs and achieves community detection accuracy comparable to Ricci flow at a small fraction of the computational cost.
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The Ricci flow with prescribed curvature on graphs
A discrete Ricci flow on graphs converges exponentially to prescribed Lin-Lu-Yau curvatures iff attainable, with an explicit max-edge-density condition for constant curvature on girth-at-least-6 graphs.
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A Classification of Positive-Curvature Discrete Einstein Metrics on Trees
Classification of finite trees with positive-curvature discrete Einstein metrics via λ_max(R_T)<0, giving explicit endpoint families for long-spine caterpillars and exhaustive algebraic verification for short spines.
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The Calabi flow with prescribed curvature on finite graphs
The Calabi flow on finite graphs converges globally if and only if a weight function exists realizing the prescribed curvature, with convergence for constant curvature under topological conditions.
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Discrete Einstein metrics on trees
Existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature is established via Perron-Frobenius theory, with positive curvature possible only on caterpillar trees and edge weights decreasing radially from the maximal edge.