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.
Evolution of weights on a connected finite graph
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
Introduces local entropy flow and cohesion flow on graphs, proves global existence and uniqueness of solutions, studies asymptotics, and applies the flows to community detection and node classification with competitive empirical results versus Ricci flows.
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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The Ollivier Ricci flow with prescribed curvature on infinite graphs
Existence, uniqueness, and convergence of the Ollivier Ricci flow with prescribed curvature are established on infinite graphs with girth at least 6.
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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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Evolving edge weights via local entropy flow and cohesion flow on graphs
Introduces local entropy flow and cohesion flow on graphs, proves global existence and uniqueness of solutions, studies asymptotics, and applies the flows to community detection and node classification with competitive empirical results versus Ricci flows.