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
6 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, uniqueness, and convergence of the Ollivier Ricci flow with prescribed curvature are established on infinite graphs with girth at least 6.
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.
Complete classification of finite trees with positive-curvature discrete Einstein metrics via the Lin-Lu-Yau Ricci curvature, giving explicit endpoint families for long caterpillars and exhaustive checks for short spines plus the zero-curvature cases.