Optimal community detection in dense bipartite graphs | Paper Citation Record

Observation c6e1d7e9-00dd-4f53-bfc3-0756ca1214c8 · outbound

This paper cites Community detection and stochastic block models: recent developments.

Optimal community detection in dense bipartite graphs Community detection and stochastic block models: recent developments

Reference 1

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This paper cites Community detection in general stochastic block models: Fun- damental limits and efficient algorithms for recovery.

Optimal community detection in dense bipartite graphs Community detection in general stochastic block models: Fun- damental limits and efficient algorithms for recovery

Reference 2

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This paper cites Statistical mechanics of complex networks.

Optimal community detection in dense bipartite graphs Statistical mechanics of complex networks

Reference 3

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This paper cites GLOBAL TESTING UNDER SPARSE ALTERNATIVES: ANOVA, MULTIPLE COMPARISONS AND THE HIGHER CRITICISM.

Optimal community detection in dense bipartite graphs GLOBAL TESTING UNDER SPARSE ALTERNATIVES: ANOVA, MULTIPLE COMPARISONS AND THE HIGHER CRITICISM

Reference 4

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This paper cites Community detection in dense random networks.

Optimal community detection in dense bipartite graphs Community detection in dense random networks

Reference 5

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This paper cites The sparse Poisson means model.

Optimal community detection in dense bipartite graphs The sparse Poisson means model

Reference 6

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This paper cites Contiguity and non-reconstruction results for planted partition models: the dense case.

Optimal community detection in dense bipartite graphs Contiguity and non-reconstruction results for planted partition models: the dense case

Reference 7

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This paper cites Optimal hypothesis testing for stochastic block models with growing degrees.

Optimal community detection in dense bipartite graphs Optimal hypothesis testing for stochastic block models with growing degrees

Reference 8

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This paper cites Information-theoretic thresholds for community detection in sparse networks.

Optimal community detection in dense bipartite graphs Information-theoretic thresholds for community detection in sparse networks

Reference 9

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Observation 6132a4b5-1ec7-4a62-983f-8bb45cbea1c9 · outbound

This paper cites Network biology: understanding the cell’s functional organization.

Optimal community detection in dense bipartite graphs Network biology: understanding the cell’s functional organization

Reference 10

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This paper cites Non-asymptotic minimax rates of testing in signal detection.

Optimal community detection in dense bipartite graphs Non-asymptotic minimax rates of testing in signal detection

Reference 11

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This paper cites Optimal detection of sparse principal components in high dimension.

Optimal community detection in dense bipartite graphs Optimal detection of sparse principal components in high dimension

Reference 12

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This paper cites Reducibility and computational lower bounds for problems with planted sparse structure.

Optimal community detection in dense bipartite graphs Reducibility and computational lower bounds for problems with planted sparse structure

Reference 13

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Observation ffc921e2-c9a3-4141-a0e1-e8020ff1779a · outbound

This paper cites Phase transitions for detecting latent geometry in random graphs.

Optimal community detection in dense bipartite graphs Phase transitions for detecting latent geometry in random graphs

Reference 14

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This paper cites Testing for high-dimensional geometry in random graphs.

Optimal community detection in dense bipartite graphs Testing for high-dimensional geometry in random graphs

Reference 15

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This paper cites Detection of a sparse submatrix of a high-dimensional noisy matrix.

Optimal community detection in dense bipartite graphs Detection of a sparse submatrix of a high-dimensional noisy matrix

Reference 16

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This paper cites Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices.

Optimal community detection in dense bipartite graphs Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices

Reference 17

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This paper cites Goodness-of-fit testing for Hölder-continuous densities: Sharp local minimax rates.

Optimal community detection in dense bipartite graphs Goodness-of-fit testing for Hölder-continuous densities: Sharp local minimax rates

Reference 18

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This paper cites Sharp local minimax rates for goodness-of-fit testing in multivariate binomial and Poisson families and in multinomials.

Optimal community detection in dense bipartite graphs Sharp local minimax rates for goodness-of-fit testing in multivariate binomial and Poisson families and in multinomials

Reference 19

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Observation 8d6a6551-7961-4e3e-83bf-ac4cc0656132 · outbound

This paper cites Sparse signal detection in heteroscedastic Gaussian sequence models: sharp minimax rates.

Optimal community detection in dense bipartite graphs Sparse signal detection in heteroscedastic Gaussian sequence models: sharp minimax rates

Reference 20

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This paper cites Graph partitioning via adaptive spectral techniques.

Optimal community detection in dense bipartite graphs Graph partitioning via adaptive spectral techniques

Reference 21

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This paper cites Minimax estimation of linear and quadratic functionals on sparsity classes.

Optimal community detection in dense bipartite graphs Minimax estimation of linear and quadratic functionals on sparsity classes

Reference 22

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This paper cites Detection and recovery of hidden submatrices.

Optimal community detection in dense bipartite graphs Detection and recovery of hidden submatrices

Reference 23

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Observation 5d588ef4-14bd-4dce-a2f4-bc35a7d0db7d · outbound

This paper cites Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications.

Optimal community detection in dense bipartite graphs Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

Reference 24

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Observation c9ad162c-ab8e-40da-bb57-c5c74bea0045 · outbound

This paper cites Community detection in complex networks: From statistical foundations to data science applications.

Optimal community detection in dense bipartite graphs Community detection in complex networks: From statistical foundations to data science applications

Reference 25

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Observation 90bd959c-ad27-40bc-a1e5-f59f9d7d62bf · outbound

This paper cites Random geometric graph: Some recent developments and perspectives.

Optimal community detection in dense bipartite graphs Random geometric graph: Some recent developments and perspectives

Reference 26

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Observation 5218d1af-0a8e-40ed-9e19-279526d140c7 · outbound

This paper cites Detecting Arbitrary Planted Subgraphs in Random Graphs.

Optimal community detection in dense bipartite graphs Detecting Arbitrary Planted Subgraphs in Random Graphs

Reference 27

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This paper cites 20 years of network community detection.

Optimal community detection in dense bipartite graphs 20 years of network community detection

Reference 28

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Observation f666da97-33be-4d2b-85bc-e10b4cd1a9dd · outbound

This paper cites Testing Network Structure Using Relations Between Small Subgraph Probabilities.

Optimal community detection in dense bipartite graphs Testing Network Structure Using Relations Between Small Subgraph Probabilities

Reference 29

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This paper cites Community detection in degree-corrected block models.

Optimal community detection in dense bipartite graphs Community detection in degree-corrected block models

Reference 30

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Observation c4c0e581-7571-4732-bf8a-774df4319d3f · outbound

This paper cites Community structure in social and biological networks.

Optimal community detection in dense bipartite graphs Community structure in social and biological networks

Reference 31

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Observation 8994905a-cb40-4822-842c-e66fe9fc8429 · outbound

This paper cites Computational lower bounds for community detection on random graphs.

Optimal community detection in dense bipartite graphs Computational lower bounds for community detection on random graphs

Reference 32

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Observation 23241233-2736-4c75-a60e-ca263744a733 · outbound

This paper cites Information limits for recovering a hidden community.

Optimal community detection in dense bipartite graphs Information limits for recovering a hidden community

Reference 33

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This paper cites The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions.

Optimal community detection in dense bipartite graphs The smallest uniform upper bound on the distance between the mean and the median of the binomial and Poisson distributions

Reference 34

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This paper cites Random subgraph detection using queries.

Optimal community detection in dense bipartite graphs Random subgraph detection using queries

Reference 35

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This paper cites Minimax testing of nonparametric hypotheses on a distribution density in the L_p metrics.

Optimal community detection in dense bipartite graphs Minimax testing of nonparametric hypotheses on a distribution density in the L_p metrics

Reference 36

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Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 37

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This paper cites Detection boundary in sparse regression.

Optimal community detection in dense bipartite graphs Detection boundary in sparse regression

Reference 38

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This paper cites On the minimax nonparametric detection of signals in white gaussian noise.

Optimal community detection in dense bipartite graphs On the minimax nonparametric detection of signals in white gaussian noise

Reference 39

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Observation 0df3067a-a993-476d-b4a6-68d682caa809 · outbound

This paper cites Asymptotic equivalence and contiguity of some random graphs.

Optimal community detection in dense bipartite graphs Asymptotic equivalence and contiguity of some random graphs

Reference 40

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Observation a5fab890-45e9-4945-a90d-bc076fe5f5a7 · outbound

This paper cites Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts.

Optimal community detection in dense bipartite graphs Locally sharp goodness-of-fit testing in sup norm for high-dimensional counts

Reference 41

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Observation 107fb984-8705-43bf-9dcb-1d5601f0ba67 · outbound

This paper cites Minimax rates for sparse signal detection under correlation.

Optimal community detection in dense bipartite graphs Minimax rates for sparse signal detection under correlation

Reference 42

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Observation cf21c7e6-9efd-4d66-bead-58ecc7f416c2 · outbound

This paper cites Sparsity meets correlation in Gaussian sequence model.

Optimal community detection in dense bipartite graphs Sparsity meets correlation in Gaussian sequence model

Reference 43

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Observation 1b72146e-ac60-4d8e-9c47-dafcb27ca474 · outbound

This paper cites Convergence of estimates under dimensionality restrictions.

Optimal community detection in dense bipartite graphs Convergence of estimates under dimensionality restrictions

Reference 44

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Observation b45c8203-fdf3-43f6-998b-a138d4b577bb · outbound

This paper cites Minimax rates in sparse, high-dimensional change point detection.

Optimal community detection in dense bipartite graphs Minimax rates in sparse, high-dimensional change point detection

Reference 45

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Observation 8dc012a0-c463-4366-936b-aa0907d82b6c · outbound

This paper cites Phase transition in noisy high-dimensional random geometric graphs.

Optimal community detection in dense bipartite graphs Phase transition in noisy high-dimensional random geometric graphs

Reference 46

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Observation 7fb9336a-a38b-4d1f-9f83-c6b00d848bd1 · outbound

This paper cites Tensor clustering with planted structures: Statistical optimality and computational limits.

Optimal community detection in dense bipartite graphs Tensor clustering with planted structures: Statistical optimality and computational limits

Reference 47

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Observation f163aa91-6c88-469d-a5d6-ff8e9a96b39e · outbound

This paper cites COMPUTATIONAL BARRIERS IN MINIMAX SUBMATRIX DETECTION.

Optimal community detection in dense bipartite graphs COMPUTATIONAL BARRIERS IN MINIMAX SUBMATRIX DETECTION

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:30.416795Z

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Observation e7f234c0-42bc-4271-84b8-3a0e4f04c960 · outbound

This paper cites Bipartite graphs and recommendation systems.

Optimal community detection in dense bipartite graphs Bipartite graphs and recommendation systems

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:30.160820Z

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Observation 6a244c24-82a5-429b-87ad-fa47f3c3e431 · outbound

This paper cites Community detection thresholds and the weak Ramanujan property.

Optimal community detection in dense bipartite graphs Community detection thresholds and the weak Ramanujan property

Reference 50

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Observation e5afa8d5-9021-4a0c-b642-506545947df6 · outbound

This paper cites A proof of the block model threshold conjecture.

Optimal community detection in dense bipartite graphs A proof of the block model threshold conjecture

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:29.723237Z

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Observation e6437e9e-fb92-474e-aff0-c383187961ea · outbound

This paper cites Belief propagation, robust reconstruction and optimal recovery of block models.

Optimal community detection in dense bipartite graphs Belief propagation, robust reconstruction and optimal recovery of block models

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:29.459385Z

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Observation 329d1491-af0e-4678-8953-59527d1562f7 · outbound

This paper cites Reconstruction and estimation in the planted partition model.

Optimal community detection in dense bipartite graphs Reconstruction and estimation in the planted partition model

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:29.168967Z

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Observation bb2bb8f5-d1b7-422e-9d5a-20c81b7c73ac · outbound

This paper cites Weak recovery, hypothesis testing, and mutual information in stochastic block models and planted factor graphs.

Optimal community detection in dense bipartite graphs Weak recovery, hypothesis testing, and mutual information in stochastic block models and planted factor graphs

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-07T14:44:10.681866Z

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Observation d83a56b7-eca2-4eb2-847d-267ee9b11d02 · outbound

This paper cites Uncovering the overlapping community structure of complex networks in nature and society.

Optimal community detection in dense bipartite graphs Uncovering the overlapping community structure of complex networks in nature and society

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:28.963086Z

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Observation 593316de-d974-4c83-a3d7-5b9cad726df5 · outbound

This paper cites Bipartite graphs in systems biology and medicine: a survey of methods and applications.

Optimal community detection in dense bipartite graphs Bipartite graphs in systems biology and medicine: a survey of methods and applications

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:28.744983Z

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Observation dfb36028-8bac-4e18-8d53-e1c35df5f7fe · outbound

This paper cites Bipartite graphs as models of population structures in evolutionary multiplayer games.

Optimal community detection in dense bipartite graphs Bipartite graphs as models of population structures in evolutionary multiplayer games

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:28.530567Z

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Observation 3dade95c-4b1d-4720-af7a-d273a3beb314 · outbound

This paper cites High-Dimensional Statistics.

Optimal community detection in dense bipartite graphs High-Dimensional Statistics

Reference 58

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Observation 8bb2e5c4-668f-473f-9aee-04fd45fab225 · outbound

This paper cites Modern discrete probability: An essential toolkit.

Optimal community detection in dense bipartite graphs Modern discrete probability: An essential toolkit

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:28.320421Z

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Observation d35c7597-cdfc-4504-9e2e-c57f4801f195 · outbound

This paper cites Maps of random walks on complex networks reveal community structure.

Optimal community detection in dense bipartite graphs Maps of random walks on complex networks reveal community structure

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:28.139289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bf1e4cb9-7c68-498f-a347-1c30330acd75 · outbound

This paper cites Planted Bipartite Graph Detection.

Optimal community detection in dense bipartite graphs Planted Bipartite Graph Detection

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:27.915852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 730435ab-2c10-4703-b66c-4aa713c6c18c · outbound

This paper cites Distribution inequalities for the binomial law.

Optimal community detection in dense bipartite graphs Distribution inequalities for the binomial law

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:27.743844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b7835fb1-34fb-4fba-ae63-c05a7398e66f · outbound

This paper cites Community detection in sparse random networks.

Optimal community detection in dense bipartite graphs Community detection in sparse random networks

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:27.444028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4bee0e10-f45f-4b09-89ff-c57eb53a18f9 · outbound

This paper cites Statistical Problems with Planted Structures: Information-Theoretical and Computational Limits.

Optimal community detection in dense bipartite graphs Statistical Problems with Planted Structures: Information-Theoretical and Computational Limits

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-07T14:44:11.907925Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66f750e1-608a-47cc-a862-7b8403f9876d · outbound

This paper cites Sharp detection boundaries on testing dense subhypergraph.

Optimal community detection in dense bipartite graphs Sharp detection boundaries on testing dense subhypergraph

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:27.267427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f226782d-8206-427a-b97d-4ff79e2f73c7 · outbound

This paper cites Testing community structure for hypergraphs.

Optimal community detection in dense bipartite graphs Testing community structure for hypergraphs

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:27.020841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6ec7382a-632d-4a73-a2e8-a6fc52c838d9 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:26.814132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3e5b399c-296d-4c2f-82ea-27cc6dd8e613 · outbound

This paper cites In this case, the problem roughly reduces to the sparse signal detection 20 problem in a standard Gaussian sequence model.

Optimal community detection in dense bipartite graphs In this case, the problem roughly reduces to the sparse signal detection 20 problem in a standard Gaussian sequence model

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:26.636145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4f65d398-f28e-4bf3-b18d-19ac1e2f4afc · outbound

This paper cites Then if µ2 <C−1 ∗ n1 k2 1 log ( cn2 k2 ) + cµ k2 log (C∗ 2e ) , it holds E [ exp(µ2XY )1 ( X≥⌈C∗ k2 1 n1 ⌉ )] <α.

Optimal community detection in dense bipartite graphs Then if µ2 <C−1 ∗ n1 k2 1 log ( cn2 k2 ) + cµ k2 log (C∗ 2e ) , it holds E [ exp(µ2XY )1 ( X≥⌈C∗ k2 1 n1 ⌉ )] <α

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:26.361028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 37ae9fdc-1444-4ce1-b56c-07cf91d362fe · outbound

This paper cites Then if µ2 < cµ k2 log (k2n1 log(cn2 k2 ) cµ2ek2 1 ) , it holds E [ exp(µ2XY )1 ( X≥⌈C∗ k2 1 n1 ⌉ )] <α.

Optimal community detection in dense bipartite graphs Then if µ2 < cµ k2 log (k2n1 log(cn2 k2 ) cµ2ek2 1 ) , it holds E [ exp(µ2XY )1 ( X≥⌈C∗ k2 1 n1 ⌉ )] <α

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:26.091768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8a4a0f5e-c318-4372-b195-87dba0bf9703 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 71

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:25.767424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 163f9782-330c-4537-a21d-84f546acd050 · outbound

This paper cites Thenf is increasing overA, and by our assumption onµ2, it holds µ2 <C−1 ∗ n1 k2 1 log ( cn2 k2 ) + cµ k2 log (C∗ 2e ) ≤ min k∈A f(k) ≤ min k∈A g(k).

Optimal community detection in dense bipartite graphs Thenf is increasing overA, and by our assumption onµ2, it holds µ2 <C−1 ∗ n1 k2 1 log ( cn2 k2 ) + cµ k2 log (C∗ 2e ) ≤ min k∈A f(k) ≤ min k∈A g(k)

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:25.539102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 67514e33-9d8d-422d-bd59-e834203ea3f0 · outbound

This paper cites Then by our assumption onµ2, we have µ2 < cµ k2 log (k2n1 log(cn2 k2 ) cµ2ek2 1 ) ≤ min k∈A f(k) ≤ min k∈A g(k).

Optimal community detection in dense bipartite graphs Then by our assumption onµ2, we have µ2 < cµ k2 log (k2n1 log(cn2 k2 ) cµ2ek2 1 ) ≤ min k∈A f(k) ≤ min k∈A g(k)

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:25.220439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d97f9532-5ff0-44bc-864e-12412d1e2011 · outbound

This paper cites Thenf is decreasing overA and is minimized atk =k1.

Optimal community detection in dense bipartite graphs Thenf is decreasing overA and is minimized atk =k1

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:24.906873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4b907a90-4984-4058-861b-31d78dd9aab1 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 75

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:24.673556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4886460c-8e4b-401a-9384-663d8249ae45 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:24.482973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 307178ae-7acd-474d-a8ff-f108b0b54ca8 · outbound

This paper cites 34 Proof of Lemma 8.

Optimal community detection in dense bipartite graphs 34 Proof of Lemma 8

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:24.254390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7eb85441-b3c6-45a5-80ab-05086f21311c · outbound

This paper cites We start by showing that ψ21∧ϕ12≍ψ21∧~ϕ12.

Optimal community detection in dense bipartite graphs We start by showing that ψ21∧ϕ12≍ψ21∧~ϕ12

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:24.064322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fbef75ad-250e-441f-ba4d-37b211e68624 · outbound

This paper cites Assume first thatc−1 µ k2 log ( cn2 k2 ) ≤ C∗ k2 1 n1.

Optimal community detection in dense bipartite graphs Assume first thatc−1 µ k2 log ( cn2 k2 ) ≤ C∗ k2 1 n1

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:23.857330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a77e92d6-ebac-4b97-ba5c-bdc900f5d791 · outbound

This paper cites We now prove the converse bound.

Optimal community detection in dense bipartite graphs We now prove the converse bound

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:23.609216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 672261cd-2ba8-4817-894d-f0b4b29d624c · outbound

This paper cites Hence, for any α> 0, there exists a constantc′ µ > 0 such that, wheneverµ2≤c′ µR, we have E [ exp(µ2XY )1 ( 1∨C∗ k2 1 n1 ≤X≤k1∧ k2 log (n1k2 k2 1 ) )] <α.

Optimal community detection in dense bipartite graphs Hence, for any α> 0, there exists a constantc′ µ > 0 such that, wheneverµ2≤c′ µR, we have E [ exp(µ2XY )1 ( 1∨C∗ k2 1 n1 ≤X≤k1∧ k2 log (n1k2 k2 1 ) )] <α

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:23.431419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9ed8a9b3-1e05-4244-907d-8f8fcd8327cb · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:23.312878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a4d672c9-74c5-4f70-b575-afab7cbf787a · outbound

This paper cites Proof of Lemma 9.

Optimal community detection in dense bipartite graphs Proof of Lemma 9

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:23.234682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 97d1236b-9e74-4e4c-84f7-37dc6c43351f · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 84

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:23.170100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d6dec52f-941e-467c-ba42-e4137d204b1a · outbound

This paper cites Assume first thatk1≤ k2 log ( n1k2 k2 1 ).

Optimal community detection in dense bipartite graphs Assume first thatk1≤ k2 log ( n1k2 k2 1 )

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:23.014867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7e3dd590-92a2-4ce0-a8e8-76789a0dca42 · outbound

This paper cites We aim to prove thatψ21 +β12 ≳ ψ12 +β21.

Optimal community detection in dense bipartite graphs We aim to prove thatψ21 +β12 ≳ ψ12 +β21

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:22.702181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 203fcf2f-36bb-47b7-9efc-05a94ad374ec · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:22.534687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c71cd4d6-d648-4d25-91dd-af383f02b361 · outbound

This paper cites Consequently, we haveR≥ ( ψ21 +β12 ) ∧ ( ψ12 +β21 ) ∧ϕ12∧ϕ21.

Optimal community detection in dense bipartite graphs Consequently, we haveR≥ ( ψ21 +β12 ) ∧ ( ψ12 +β21 ) ∧ϕ12∧ϕ21

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:22.343802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 07d1dbb1-a111-4236-9f14-87b09887565f · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 89

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:22.165427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 96ffba5a-4421-44be-bf9e-80bf333252e2 · outbound

This paper cites Then we have ψ12 = 1 k1 log ( 1 +n2k1 k2 2 log (n1 k1 )) ≥ 1 k1 log ( 1 +n2 k2 ) ≥β12, which yields the desired result.

Optimal community detection in dense bipartite graphs Then we have ψ12 = 1 k1 log ( 1 +n2k1 k2 2 log (n1 k1 )) ≥ 1 k1 log ( 1 +n2 k2 ) ≥β12, which yields the desired result

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:22.021859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5292466e-b5a4-4969-8b82-b277790a1647 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:21.820577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 074e67eb-294a-4ce6-a298-a04901917459 · outbound

This paper cites Consequently, we haveR≥ ( ψ21 +β12 ) ∧ ( ψ12 +β21 ) ∧ϕ12∧ϕ21.

Optimal community detection in dense bipartite graphs Consequently, we haveR≥ ( ψ21 +β12 ) ∧ ( ψ12 +β21 ) ∧ϕ12∧ϕ21

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:21.615588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 632febab-bd6a-422c-8f5a-efc039f5a0bc · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 93

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:21.436748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b98879e4-e681-46ab-8227-5923802a2b5c · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 94

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:21.284379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation af003ea8-7c47-41cf-87a7-69e0bd6a0287 · outbound

This paper cites Similarly, if˜R =ϕ21 and n1 >k 2 1, the result follows by Lemma 16.

Optimal community detection in dense bipartite graphs Similarly, if˜R =ϕ21 and n1 >k 2 1, the result follows by Lemma 16

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:21.152317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e87b9b80-4cce-45f3-add8-42a898bf4f2b · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 96

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:20.852763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 15f768dc-e733-49fb-aed3-71dc40d19388 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 97

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:20.561029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation be24df4f-f6c0-4888-9ecb-f21ad90a97b3 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 98

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:20.326190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9f3ba37b-7d5e-46d5-b1a6-ff5cf229439e · outbound

This paper cites Proof of Lemma 32.

Optimal community detection in dense bipartite graphs Proof of Lemma 32

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:44:20.073514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4efed9b9-b931-4b23-8dc8-2d039b57a038 · outbound

This paper cites an unresolved cited work.

Optimal community detection in dense bipartite graphs Unresolved cited work

Reference 100

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:44:19.715887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Reference resolution

Outbound references

Pith citing papers