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.
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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.
Existence and uniqueness of discrete Einstein metrics on trees is established under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory, with a sharp upper bound on the largest eigenvalue and the implication that positive-curvature cases require caterpillar trees.
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.
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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Discrete Einstein metrics on trees
Existence and uniqueness of discrete Einstein metrics on trees is established under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory, with a sharp upper bound on the largest eigenvalue and the implication that positive-curvature cases require caterpillar trees.
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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.
- Positive-Curvature Discrete Einstein Metrics on Trees