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Paper Citation Record · LEDGER

Lower Ricci Curvature for Hypergraphs

As of 8 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:2506.03943.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.03943 v1

Coverage vector

measured 60 of 60 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:00:03.186154Z

measured 60 of 60 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

60 of 60 outbound references displayed

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External citation measurements

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Outbound references

Observation 097e1f05-7e91-4f0c-8429-1e8e96e52829 · outbound

This paper cites The temporal dynamics of group interactions in higher-order social networks.Nature Communications, 15(1):7391, 2024.

Lower Ricci Curvature for Hypergraphs The temporal dynamics of group interactions in higher-order social networks.Nature Communications, 15(1):7391, 2024

Reference 1

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation b9f4beb4-374c-4df6-a6bf-a023057af022 · outbound

This paper cites Social influence maximization in hypergraph in social networks.IEEE Transactions on Network Science and Engineering, 6(4):801–811, 2018.

Lower Ricci Curvature for Hypergraphs Social influence maximization in hypergraph in social networks.IEEE Transactions on Network Science and Engineering, 6(4):801–811, 2018

Reference 2

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Observation c70adcea-708a-4cb8-9bcb-ec665f3c6703 · outbound

This paper cites Hypergraph topological quantities for tagged social networks.

Lower Ricci Curvature for Hypergraphs Hypergraph topological quantities for tagged social networks

Reference 3

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Observation ce57f889-50e1-4c28-a36d-b9ce9d853fcd · outbound

This paper cites Hypergraph collaborative network on vertices and hyperedges.IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3):3245–3258, 2022.

Lower Ricci Curvature for Hypergraphs Hypergraph collaborative network on vertices and hyperedges.IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3):3245–3258, 2022

Reference 4

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raw_fallback, observed 2026-08-07T11:00:03.600085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.018922Z digest=sha256:beea657d73e638754ba261d2d3b26c73f83628f3cad59dbc3734d54a3780f798

Observation 6ad79337-e718-4f61-bab5-3027632ae36d · outbound

This paper cites Relational hyperevent models for the coevolution of coauthoring and citation networks.Journal of the Royal Statistical Society Series A: Statistics in Society, 188(2):583–607, 2025.

Lower Ricci Curvature for Hypergraphs Relational hyperevent models for the coevolution of coauthoring and citation networks.Journal of the Royal Statistical Society Series A: Statistics in Society, 188(2):583–607, 2025

Reference 5

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.022613Z digest=sha256:fde9ed4acbc0bde1aa2b9f8a24a733fbd89b9cafb6eb9e797db2d13d61d3ebca

Observation ba94aee4-8a66-4258-9a80-8768af85e51a · outbound

This paper cites Integration of protein sequence and protein–protein interaction data by hypergraph learning to identify novel protein complexes.

Lower Ricci Curvature for Hypergraphs Integration of protein sequence and protein–protein interaction data by hypergraph learning to identify novel protein complexes

Reference 6

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source=pdf_text observed=2026-08-07T11:00:03.025548Z digest=sha256:2149238e2bcaa2ba167d9c3482c156585578a27fe134f019911077824bb2bde5

Observation b46c4e97-5554-4d99-a10c-dc665b7a36be · outbound

This paper cites A hierarchical graph neural network framework for predicting protein-protein interaction modulators with functional group information and hypergraph structure.

Lower Ricci Curvature for Hypergraphs A hierarchical graph neural network framework for predicting protein-protein interaction modulators with functional group information and hypergraph structure

Reference 7

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raw_fallback, observed 2026-08-07T11:00:03.576350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.028277Z digest=sha256:ca1c324207857d903351938aeb3ddd4c2ca336c717132f38d00e6479da605f2e

Observation f713a8de-b207-48de-bf5e-d3e80ded3a40 · outbound

This paper cites Elsevier, 1984.

Lower Ricci Curvature for Hypergraphs Elsevier, 1984

Reference 8

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source=pdf_text observed=2026-08-07T11:00:03.031251Z digest=sha256:f1f32ecea3790b4523fdf71ddf897b2062d28d71be3e51a188b55e47ae4cfee5

Observation b70245fb-4358-456f-afd0-f9d95ff8df9d · outbound

This paper cites Hypergraph theory.An introduction.

Lower Ricci Curvature for Hypergraphs Hypergraph theory.An introduction

Reference 9

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source=pdf_text observed=2026-08-07T11:00:03.034263Z digest=sha256:e9cd5da8afde420aadf6025ee75eb65d480bddba704242822ad8a763567d7967

Observation de1a9480-0e37-4ccc-aaa0-a57e95ed1100 · outbound

This paper cites Tensor entropy for uniform hypergraphs.IEEE Transactions on Network Science and Engineering, 7(4):2889–2900, 2020.

Lower Ricci Curvature for Hypergraphs Tensor entropy for uniform hypergraphs.IEEE Transactions on Network Science and Engineering, 7(4):2889–2900, 2020

Reference 10

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.037223Z digest=sha256:2301d2359a8d0caeebb68ebd23fd8b2eeb383828f2fe6fcd14ee3b25f9ac1a38

Observation d5e19c6f-fc65-4022-8416-c31b933113bf · outbound

This paper cites Controllability of hypergraphs.IEEE Transactions on Network Science and Engineering, 8(2):1646–1657, 2021.

Lower Ricci Curvature for Hypergraphs Controllability of hypergraphs.IEEE Transactions on Network Science and Engineering, 8(2):1646–1657, 2021

Reference 11

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Observation 92d2dbff-15ed-4407-bd54-0c29a189bdc6 · outbound

This paper cites Diversities and the geometry of hypergraphs.Discrete Mathematics & Theoretical Computer Science, 16(PRIMA 2013), 2014.

Lower Ricci Curvature for Hypergraphs Diversities and the geometry of hypergraphs.Discrete Mathematics & Theoretical Computer Science, 16(PRIMA 2013), 2014

Reference 12

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation cd09cba7-7817-4f3a-9452-c8da6ee49434 · outbound

This paper cites Graph geometry interaction learning.

Lower Ricci Curvature for Hypergraphs Graph geometry interaction learning

Reference 13

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source=pdf_text observed=2026-08-07T11:00:03.045518Z digest=sha256:7d09f0f2a906fbfd4335d7c11bef8a16135f89b62eca7eb1b8fa4e693ee8bba0

Observation 9d13a6b2-b289-448e-8a27-d31f379a9fca · outbound

This paper cites Network geometry inference using common neighbors.Physical Review E, 92(2):022807, 2015.

Lower Ricci Curvature for Hypergraphs Network geometry inference using common neighbors.Physical Review E, 92(2):022807, 2015

Reference 14

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raw_fallback, observed 2026-08-07T11:00:03.533085Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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Observation d433f9c4-0449-458c-b083-02020ec464e8 · outbound

This paper cites Geometric deep learning on graphs and manifolds using mixture model cnns.

Lower Ricci Curvature for Hypergraphs Geometric deep learning on graphs and manifolds using mixture model cnns

Reference 15

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source=pdf_text observed=2026-08-07T11:00:03.051300Z digest=sha256:1edf83e723bba35483a85939346d5fbbabd62abc3e6734633dafab0ae37a2395

Observation 2fc142de-add6-4dfb-afd5-281ec45fd109 · outbound

This paper cites Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959.

Lower Ricci Curvature for Hypergraphs Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959

Reference 16

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no resolver link, observed 2026-08-07T11:00:03.054390Z

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source=pdf_text observed=2026-08-07T11:00:03.054390Z digest=sha256:ddf85042408ca206b9cb1925df5f924644a20b19af4239c5188de7711b123229

Observation 9e6581ed-99e2-4fa3-bfaa-659748124343 · outbound

This paper cites Curvature graph network.

Lower Ricci Curvature for Hypergraphs Curvature graph network

Reference 17

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raw_fallback, observed 2026-08-07T11:00:03.518764Z

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source=pdf_text observed=2026-08-07T11:00:03.057041Z digest=sha256:f2c1bfa1270f7075f3f6b832d9e214e492550c483c7cff0cef94ba9918d9753c

Observation 4d557e5d-c82a-47a2-972e-3aff33387169 · outbound

This paper cites Ricci curvature of Markov chains on metric spaces.Journal of Functional Analysis, 256(3):810–864, 2009.

Lower Ricci Curvature for Hypergraphs Ricci curvature of Markov chains on metric spaces.Journal of Functional Analysis, 256(3):810–864, 2009

Reference 18

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source=pdf_text observed=2026-08-07T11:00:03.059574Z digest=sha256:a466ce8ddb4b82efe995f985024a2ae79ad69e6eb11f6e6d23869b740717cdd6

Observation 37deceac-cfb1-4b46-bb31-6e4fc498bd20 · outbound

This paper cites A survey of Ricci curvature for metric spaces and Markov chains.

Lower Ricci Curvature for Hypergraphs A survey of Ricci curvature for metric spaces and Markov chains

Reference 19

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.061924Z digest=sha256:58bdce8821e4c82d4a284eb565bbb587a1b88fcf6368bf04c32ecebae40f68e8

Observation d8fef4b6-0790-4ecd-9815-1017e5a8f76e · outbound

This paper cites Ricci curvature for metric-measure spaces via optimal transport.Annals of Mathematics, pages 903–991, 2009.

Lower Ricci Curvature for Hypergraphs Ricci curvature for metric-measure spaces via optimal transport.Annals of Mathematics, pages 903–991, 2009

Reference 20

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source=pdf_text observed=2026-08-07T11:00:03.065346Z digest=sha256:a2728188fd12ec5c4432892a900c34218de4876de7e82043facaee14a42c030a

Observation ca9dc927-0383-4001-908c-2ce9977994f5 · outbound

This paper cites Ricci curvature of graphs.Tohoku Mathematical Journal, Second Series, 63(4):605–627, 2011.

Lower Ricci Curvature for Hypergraphs Ricci curvature of graphs.Tohoku Mathematical Journal, Second Series, 63(4):605–627, 2011

Reference 21

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source=pdf_text observed=2026-08-07T11:00:03.068698Z digest=sha256:4f9fbaf45d5c88513eecb11099220b8bc74b8e0e8df1077340be75256f3b6a66

Observation 5b6458e4-64fe-4ff9-959d-aaf27e7f3549 · outbound

This paper cites Mitigating over-smoothing and over-squashing using augmentations of Forman- Ricci curvature.

Lower Ricci Curvature for Hypergraphs Mitigating over-smoothing and over-squashing using augmentations of Forman- Ricci curvature

Reference 22

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source=pdf_text observed=2026-08-07T11:00:03.072442Z digest=sha256:e07d9597337fd040f1a5c611b9f1599404bd630bcb2dee2a69b3163ce1b9bffc

Observation 7533efa8-3e41-42bf-86c8-bba3e6ac8633 · outbound

This paper cites Forman curvature for complex networks.Journal of Statistical Mechanics: Theory and Experiment, 2016(6):063206, 2016.

Lower Ricci Curvature for Hypergraphs Forman curvature for complex networks.Journal of Statistical Mechanics: Theory and Experiment, 2016(6):063206, 2016

Reference 23

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raw_fallback, observed 2026-08-07T11:00:03.474963Z

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Observation 399e97b1-686e-447c-96e7-813a576670be · outbound

This paper cites Ollivier-Ricci curvature-based method to community detection in complex networks.Scientific reports, 9(1):9800, 2019.

Lower Ricci Curvature for Hypergraphs Ollivier-Ricci curvature-based method to community detection in complex networks.Scientific reports, 9(1):9800, 2019

Reference 24

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source=pdf_text observed=2026-08-07T11:00:03.078009Z digest=sha256:a98feca08d0f35fc6989e7e6a2abe31695cc897a5a332b2e5f902f6925af7416

Observation 5335ad1a-14d4-439f-99cd-f097ec835354 · outbound

This paper cites Lower Ricci Curvature for Efficient Community Detection.

Lower Ricci Curvature for Hypergraphs Lower Ricci Curvature for Efficient Community Detection

Reference 25

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no resolver link, observed 2026-08-07T11:00:03.081694Z

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source=pdf_text observed=2026-08-07T11:00:03.081694Z digest=sha256:4410200f5196dfe8364d8e92f64010c437197dae23629313de269a44381321a1

Observation 92a548f5-7068-4044-8737-81661155ba37 · outbound

This paper cites Curvature-based clustering on graphs.Journal of Machine Learning Research, 26(52):1–67, 2025.

Lower Ricci Curvature for Hypergraphs Curvature-based clustering on graphs.Journal of Machine Learning Research, 26(52):1–67, 2025

Reference 26

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raw_fallback, observed 2026-08-07T11:00:03.463974Z

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Observation efcb088e-de22-4f37-8a51-df97d35dd54c · outbound

This paper cites Mixed-membership community detection via line graph curvature.

Lower Ricci Curvature for Hypergraphs Mixed-membership community detection via line graph curvature

Reference 27

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raw_fallback, observed 2026-08-07T11:00:03.457316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.087596Z digest=sha256:3e2ac4fb3aa63a3adba1960ffc08dce0c8f0ff81b5e1a9c980b7c90b35838037

Observation c17809c2-6cd9-4fa0-8d71-c6ad069269f1 · outbound

This paper cites Graph curvature for differentiating cancer networks.Scientific reports, 5(1):12323, 2015.

Lower Ricci Curvature for Hypergraphs Graph curvature for differentiating cancer networks.Scientific reports, 5(1):12323, 2015

Reference 28

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verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.450686Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.091869Z digest=sha256:26e003c710adea365b1ddd1e6225b25e64eb0eb85b2625512bf88184fe316e1a

Observation 91b55ebd-e98a-43d1-a1c6-9b3891e7ae26 · outbound

This paper cites Characterizing cancer drug response and biological correlates: a geometric network approach.Scientific reports, 8(1):6402, 2018.

Lower Ricci Curvature for Hypergraphs Characterizing cancer drug response and biological correlates: a geometric network approach.Scientific reports, 8(1):6402, 2018

Reference 29

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raw_fallback, observed 2026-08-07T11:00:03.443413Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.094989Z digest=sha256:5a6453e90f91951b294186fafb8c1c571e37ab0cc5315713f096fa5296ef11ec

Observation 17b57633-397a-4404-8706-b2068fc12a89 · outbound

This paper cites an unresolved cited work.

Lower Ricci Curvature for Hypergraphs Unresolved cited work

Reference 30

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unresolved
raw_fallback, observed 2026-08-07T11:00:03.435655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.097911Z digest=sha256:6ed91a9f53b459e87d8608ebd41423babc17ddec2108aaf6645fba92ce3b4555

Observation f2c3aa9f-b208-4fc5-ae51-6d97531bee22 · outbound

This paper cites Georgiou, Allen Tannenbaum, and Christophe Lenglet.

Lower Ricci Curvature for Hypergraphs Georgiou, Allen Tannenbaum, and Christophe Lenglet

Reference 31

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verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.429204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.100839Z digest=sha256:4dcb057092abc39de23f161b274c8ab7514e700a5ff1442fca2d99ceb280875d

Observation 23aceb2b-9c32-42e6-a1f0-59361e1dc169 · outbound

This paper cites Measuring road network topology vulnerability by Ricci curvature.Physica A: Statistical Mechanics and Its Applications, 527:121071, 2019.

Lower Ricci Curvature for Hypergraphs Measuring road network topology vulnerability by Ricci curvature.Physica A: Statistical Mechanics and Its Applications, 527:121071, 2019

Reference 32

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raw_fallback, observed 2026-08-07T11:00:03.421571Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.103863Z digest=sha256:ce93cd57ba10c410171e704466a48084e699648071ed4a660c5e1741c803fc24

Observation 0c44f144-9fa3-40b1-8181-b82faa0a6bf8 · outbound

This paper cites Vulnerability analysis method based on network and copula entropy.Entropy, 26(3):192, 2024.

Lower Ricci Curvature for Hypergraphs Vulnerability analysis method based on network and copula entropy.Entropy, 26(3):192, 2024

Reference 33

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raw_fallback, observed 2026-08-07T11:00:03.413955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.106810Z digest=sha256:8a932c27174240d98cd32a9c7c904d8bc832e691c9ce890b797aa803aa2ac3b5

Observation 69a9a76b-70d4-4517-8dcb-fb9e1fc52972 · outbound

This paper cites Analyzing neural network robustness using graph curvature.

Lower Ricci Curvature for Hypergraphs Analyzing neural network robustness using graph curvature

Reference 34

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verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.406657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.109545Z digest=sha256:06800365d6fbbf8582e5f655cc8b8fb4472b5882c2a8ae93064adc0a4bce422c

Observation 12e12ae9-9ad2-4a66-abf8-a2b586dfd701 · outbound

This paper cites Ollivier-Ricci curvature approach to cost-effective power grid congestion management.

Lower Ricci Curvature for Hypergraphs Ollivier-Ricci curvature approach to cost-effective power grid congestion management

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.399476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.112451Z digest=sha256:8f9fd4775766f66abdaf4a68c09738d23bb498fbafa820b8eacd0e7b2efba40f

Observation 935cb4c4-4453-4426-87ef-32934446eae3 · outbound

This paper cites Understanding over-squashing and bottlenecks on graphs via curvature.

Lower Ricci Curvature for Hypergraphs Understanding over-squashing and bottlenecks on graphs via curvature

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-07T11:00:03.115446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:00:03.115446Z digest=sha256:71edb5a8d95d02df03a1933607b7c184162532c7292af1a4fa6fe7dcede48d49

Observation 6e8b5468-f489-4d51-91e5-79fcde809335 · outbound

This paper cites Curvature graph neural network.Information Sciences, 592:50–66, 2022.

Lower Ricci Curvature for Hypergraphs Curvature graph neural network.Information Sciences, 592:50–66, 2022

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.391179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.118510Z digest=sha256:aa0adfbe4abbe6bc4909f9514aa574626e4f7560a7437f33e86f545d76c8b9d7

Observation 9c7b9117-b188-4c61-a457-a86222ad8288 · outbound

This paper cites A self-supervised mixed- curvature graph neural network.

Lower Ricci Curvature for Hypergraphs A self-supervised mixed- curvature graph neural network

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.383431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.121448Z digest=sha256:d52b5cd81c26061ca8d0c0fca9caa7e048cafca0929d1f6ceb7d6209b4c858c9

Observation bcf43254-8f12-4003-a1bd-bbfeb00aa024 · outbound

This paper cites Curvdrop: A Ricci curva- ture based approach to prevent graph neural networks from over-smoothing and over-squashing.

Lower Ricci Curvature for Hypergraphs Curvdrop: A Ricci curva- ture based approach to prevent graph neural networks from over-smoothing and over-squashing

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.376446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.124791Z digest=sha256:2f35391e1440b6454ee7ca20fb19a111abecde2422daf01f77731c88660bbf90

Observation c675823d-bc8e-4e51-b090-9c025871c910 · outbound

This paper cites Ricci curvature of the internet topology.

Lower Ricci Curvature for Hypergraphs Ricci curvature of the internet topology

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.368898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.127458Z digest=sha256:653ff9275460bf410ef86c969fc21035fe6eafa4c9200742e72ac81ecfd5a5fc

Observation fc69a94d-1f0d-4475-a3ce-bc5919df4100 · outbound

This paper cites Comparative analysis of two discretizations of Ricci curvature for complex networks.Scientific reports, 8(1):8650, 2018.

Lower Ricci Curvature for Hypergraphs Comparative analysis of two discretizations of Ricci curvature for complex networks.Scientific reports, 8(1):8650, 2018

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.362628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.130201Z digest=sha256:0a1f6078c5a096ca39972b2a9fad14abb90c7ef047c0e5725da162839d9469f0

Observation 01e8d01c-65f2-430a-9bfd-a23c691d273b · outbound

This paper cites ORCO: Ollivier-Ricci Curvature-Omics—an unsupervised method for analyzing robustness in biological systems.Bioinformatics, 41(3):btaf093, 2025.

Lower Ricci Curvature for Hypergraphs ORCO: Ollivier-Ricci Curvature-Omics—an unsupervised method for analyzing robustness in biological systems.Bioinformatics, 41(3):btaf093, 2025

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.355657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.133053Z digest=sha256:34346350733c7347932fbd626f32c5c50481677032f43c9f40c365b755f43ebf

Observation f49b4edb-5202-4ccf-b226-09a01ec47a45 · outbound

This paper cites Inferring functional communities from partially observed biological networks exploiting geometric topology and side information.Scientific Reports, 12(1):10883, 2022.

Lower Ricci Curvature for Hypergraphs Inferring functional communities from partially observed biological networks exploiting geometric topology and side information.Scientific Reports, 12(1):10883, 2022

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.347328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.135650Z digest=sha256:357a77f6715e25711831eb1b8ebea90a6095b08a7237f4b211037956b063a40d

Observation 1151ea08-2625-4417-a85e-5107c7156b5e · outbound

This paper cites Ollivier Ricci curvature of directed hypergraphs.Scientific Reports, 10(1):12466, 2020.

Lower Ricci Curvature for Hypergraphs Ollivier Ricci curvature of directed hypergraphs.Scientific Reports, 10(1):12466, 2020

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.339437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.138497Z digest=sha256:668661df22ba568c0fcb08cd11850c34d501900d532cb17eee3ae26fa60b8c3e

Observation 91c74a60-c680-4774-90fe-d1fc6ba7ccdc · outbound

This paper cites Ollivier-Ricci curvature for hypergraphs: A unified framework.

Lower Ricci Curvature for Hypergraphs Ollivier-Ricci curvature for hypergraphs: A unified framework

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.331142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.141467Z digest=sha256:8b41acf36f3cf078ef8911909c721aac4f7668102bcde68e411bcbde6fdf49ed

Observation 22cecd38-875d-427e-bfa3-297a279ef8fd · outbound

This paper cites Forman–Ricci curvature for hypergraphs.

Lower Ricci Curvature for Hypergraphs Forman–Ricci curvature for hypergraphs

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.322797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.144554Z digest=sha256:4d4339ffbec27a7952fcfa59fff06ad337ce89336bf9b19f599363248b2622ab

Observation 4f20f75e-b9aa-42c2-9ebb-a2794c3005ea · outbound

This paper cites Consistency of spectral partitioning of uniform hypergraphs under planted partition model.Advances in Neural Information Processing Systems, 27, 2014.

Lower Ricci Curvature for Hypergraphs Consistency of spectral partitioning of uniform hypergraphs under planted partition model.Advances in Neural Information Processing Systems, 27, 2014

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.314346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.147055Z digest=sha256:139f8b2051080252663fa76a5f6b96efca4fefe5d8a341772f70d62e0d27f924

Observation 40656400-3af5-4963-ad16-4fae280357aa · outbound

This paper cites Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys.PLOS ONE, 10(9):e0136497, 2015.

Lower Ricci Curvature for Hypergraphs Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys.PLOS ONE, 10(9):e0136497, 2015

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.305670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.150386Z digest=sha256:69fc6e6ee7cd88247c65aceba560aa90fa977615f662039f0e0f59c4215bb45d

Observation d0631ccb-445b-40d6-9826-5ba59a543109 · outbound

This paper cites Hypergraph clustering: from blockmodels to modularity.

Lower Ricci Curvature for Hypergraphs Hypergraph clustering: from blockmodels to modularity

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.297970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.153266Z digest=sha256:82b7831dfe1482e1d06f3363ec1a7581e35915e6928a2efaad0ad7f1fa44e03b

Observation 0e568a3c-5307-4e21-89dc-f5b4a563d572 · outbound

This paper cites Spring Embedders and Force Directed Graph Drawing Algorithms.

Lower Ricci Curvature for Hypergraphs Spring Embedders and Force Directed Graph Drawing Algorithms

Reference 50

Resolution
unresolved
no resolver link, observed 2026-08-07T11:00:03.156153Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:00:03.156153Z digest=sha256:e8f06a537637abff5c78a70618e44cf9ac95f334183990ac79e7706ce1548ea1

Observation ba760bb3-3e0c-4fc0-971d-5cc06f19bcfd · outbound

This paper cites Co-citation and co-authorship networks of statisticians.Journal of Business & Economic Statistics, 40(2):469–485, 2022.

Lower Ricci Curvature for Hypergraphs Co-citation and co-authorship networks of statisticians.Journal of Business & Economic Statistics, 40(2):469–485, 2022

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.290870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.160062Z digest=sha256:781efddb9f8ade54f81509269d6e5ae18f1dc570aaa75d24448b02af59a81120

Observation a8d134f3-d351-413d-bdfe-48e3382f4481 · outbound

This paper cites Clustering in graphs and hypergraphs with categorical edge labels.

Lower Ricci Curvature for Hypergraphs Clustering in graphs and hypergraphs with categorical edge labels

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.283341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.162634Z digest=sha256:dd715a513e87c46a2c50c59ed6cfeaa50ddd7ace7902ce323117cad79d0d17d3

Observation 6e61bfcc-ce49-468e-a29e-2ff617c55319 · outbound

This paper cites An overview of microsoft academic service (MAS) and applications.

Lower Ricci Curvature for Hypergraphs An overview of microsoft academic service (MAS) and applications

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.275566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.164948Z digest=sha256:357f07b1709c17451f8dc7567acd77137d18f2a4a5fc1585e4860695f75ac176

Observation 3d8623ba-ae7d-4420-b871-955455f87c17 · outbound

This paper cites Comparing partitions.Journal of classification, 2:193–218, 1985.

Lower Ricci Curvature for Hypergraphs Comparing partitions.Journal of classification, 2:193–218, 1985

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-07T11:00:03.168239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:00:03.168239Z digest=sha256:194a96f634c037832ffe9ac2d6bdfca70dfbadfa2fca62952ca5960b726ae0ff

Observation d201c5ce-5f6d-402c-8494-847dd6d640cb · outbound

This paper cites an unresolved cited work.

Lower Ricci Curvature for Hypergraphs Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:00:03.263391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.170772Z digest=sha256:7de8a8e823cea81940e5c7f28efb692bf1c8da9e5c0cfa5334f855e4af0c8370

Observation e2983e52-724e-4add-a4e8-4af781bbe892 · outbound

This paper cites Dually chordal graphs.SIAM journal on discrete mathematics, 11(3):437–455, 1998.

Lower Ricci Curvature for Hypergraphs Dually chordal graphs.SIAM journal on discrete mathematics, 11(3):437–455, 1998

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.255867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.173591Z digest=sha256:0a11f63e529a26cb917b0df7d8a9a65333ba0ac938aa89d8321c2e30a87f55c7

Observation 94530106-a9f2-48a3-8997-555fc12261dd · outbound

This paper cites Radial basis functions.Acta numerica, 9:1–38, 2000.

Lower Ricci Curvature for Hypergraphs Radial basis functions.Acta numerica, 9:1–38, 2000

Reference 57

Resolution
unresolved
no resolver link, observed 2026-08-07T11:00:03.176715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:00:03.176715Z digest=sha256:edf4893675f9bd576def0410891e187f7f939c7bac09195af0bff50fdf5d4fd7

Observation e20b2751-28ad-481a-9fed-e3b5e29c797a · outbound

This paper cites Kernel principal component analysis.

Lower Ricci Curvature for Hypergraphs Kernel principal component analysis

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-07T11:00:03.179404Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:00:03.179404Z digest=sha256:be330e1c5530d69a4c74f59bce27f5d7bfdef4ebd049615899ec470bc510209d

Observation 4a731698-6b75-41cb-9b49-b6a731860286 · outbound

This paper cites Some methods for classification and analysis of multivariate observations.

Lower Ricci Curvature for Hypergraphs Some methods for classification and analysis of multivariate observations

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.240816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.182758Z digest=sha256:e8ade60e04d6e2aeedf1e9b3fc48a95707c501f4d83922104ea22141bb16611a

Observation 03e8a2e2-eccf-4bb1-a4ec-b8306d83d05e · outbound

This paper cites Lower Ricci Curvature for Hypergraphs.

Lower Ricci Curvature for Hypergraphs Lower Ricci Curvature for Hypergraphs

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:00:03.232618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-07T11:00:03.186154Z digest=sha256:2a3ef43249bd788b81a8ae00c1265df0c474948a9894c4dda6f4caa05da9f896

Pith citing papers

No inbound Pith citation observations are available.