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Paper Citation Record · LEDGER

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation

As of 8 August 2026, this Paper Citation Record lists 77 of 77 outbound references and 0 inbound Pith citation observations for arXiv:2602.08785.

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

pith.paper-citation-record.v1
2602.08785 v2

Coverage vector

measured 77 of 77 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T03:20:37.558016Z

measured 77 of 77 standing notices

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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

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Source: cited_works

Reference resolution

77 of 77 outbound references displayed

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Outbound references

Observation ea25f641-edd7-4f9d-bce1-1eeccd82342b · outbound

This paper cites Trees and amenable equivalence relations.Ergodic Theory and Dynamical Systems, 10(1):1–14, 1990.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Trees and amenable equivalence relations.Ergodic Theory and Dynamical Systems, 10(1):1–14, 1990

Reference 1

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This paper cites Springer, 2005.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Springer, 2005

Reference 2

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This paper cites Characterizing the expressive power of invariant and equivariant graph neural networks.International Conference on Learning Representations, 2021.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Characterizing the expressive power of invariant and equivariant graph neural networks.International Conference on Learning Representations, 2021

Reference 3

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This paper cites Action convergence of operators and graphs.Canadian Journal of Mathematics, 74(1):72–121, 2022.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Action convergence of operators and graphs.Canadian Journal of Mathematics, 74(1):72–121, 2022

Reference 4

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Observation 60915b35-ce73-43f4-8e85-062902814264 · outbound

This paper cites Emergence of scaling in random networks.Science, 286(5439):509–512, 1999.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Emergence of scaling in random networks.Science, 286(5439):509–512, 1999

Reference 5

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This paper cites Probability and measure.A Wiley-Interscience Publica- tion, John Wiley, 118:119, 1995.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Probability and measure.A Wiley-Interscience Publica- tion, John Wiley, 118:119, 1995

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This paper cites Springer, 2007.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Springer, 2007

Reference 7

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This paper cites Fine-grained expressivity of graph neural networks.Advances in Neural Information Processing Systems, 36, 2024.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Fine-grained expressivity of graph neural networks.Advances in Neural Information Processing Systems, 36, 2024

Reference 8

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Unresolved cited work

Reference 9

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This paper cites Sparse exchangeable graphs and their limits via graphon processes.Journal of Machine Learning Research, 18(210):1–71, 2018.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Sparse exchangeable graphs and their limits via graphon processes.Journal of Machine Learning Research, 18(210):1–71, 2018

Reference 10

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This paper cites An Lp theory of sparse graph convergence ii: Ld convergence, quotients and right convergence.The Annals of Probability, 2018.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation An Lp theory of sparse graph convergence ii: Ld convergence, quotients and right convergence.The Annals of Probability, 2018

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Observation f3e418ad-9cba-4f99-9b43-ebb4285d1738 · outbound

This paper cites Convergent sequences of dense graphs i: Subgraph frequencies, metric properties and testing.Advances in Mathematics, 219(6):1801–1851, 2008.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Convergent sequences of dense graphs i: Subgraph frequencies, metric properties and testing.Advances in Mathematics, 219(6):1801–1851, 2008

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This paper cites Universal function approximation on graphs.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Universal function approximation on graphs

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This paper cites American Mathematical Society Providence, 2001.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation American Mathematical Society Providence, 2001

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This paper cites Monte carlo and quasi-monte carlo methods.Acta numerica, 7:1–49, 1998.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Monte carlo and quasi-monte carlo methods.Acta numerica, 7:1–49, 1998

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This paper cites Machine learning on graphs: A model and comprehensive taxonomy.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Machine learning on graphs: A model and comprehensive taxonomy

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This paper cites Weisfeiler-lehman meets Gromov-Wasserstein.International Conference on Machine Learning, 2022.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Weisfeiler-lehman meets Gromov-Wasserstein.International Conference on Machine Learning, 2022

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This paper cites On the equiva- lence between graph isomorphism testing and function approximation with gnns.Advances in neural information processing systems, 3, 2019.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation On the equiva- lence between graph isomorphism testing and function approximation with gnns.Advances in neural information processing systems, 3, 2019

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This paper cites Approximation by superpositions of a sigmoidal function.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Approximation by superpositions of a sigmoidal function

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Graph neural networks for social recommendation

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This paper cites John Wiley & Sons, 1999.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation John Wiley & Sons, 1999

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This paper cites Spaces in which sequences suffice.Fundamenta Mathematicae, 57(1):107–115, 1965.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Spaces in which sequences suffice.Fundamenta Mathematicae, 57(1):107–115, 1965

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation On the approximate realization of continuous mappings by neural networks.Neural networks, 2(3):183–192, 1989

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This paper cites A survey of graph neural networks for recommender systems: Challenges, methods, and directions.ACM Transactions on Recommender Systems, 1(1):1–51, 2023.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation A survey of graph neural networks for recommender systems: Challenges, methods, and directions.ACM Transactions on Recommender Systems, 1(1):1–51, 2023

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This paper cites Generalization and representational limits of graph neural networks.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Generalization and representational limits of graph neural networks

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This paper cites Expressiveness and approximation properties of graph neural networks.International Conference on Learning Representations, 2022.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Expressiveness and approximation properties of graph neural networks.International Conference on Learning Representations, 2022

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Neural message passing for quantum chemistry

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This paper cites Fractional isomorphism of graphons.Combi- natorica, 42(3):365–404, 2022.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Fractional isomorphism of graphons.Combi- natorica, 42(3):365–404, 2022

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This paper cites word2vec, node2vec, graph2vec, x2vec: Towards a theory of vector embeddings of structured data.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation word2vec, node2vec, graph2vec, x2vec: Towards a theory of vector embeddings of structured data

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This paper cites Inductive representation learning on large graphs.Advances in neural information processing systems, 30, 2017.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Inductive representation learning on large graphs.Advances in neural information processing systems, 30, 2017

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation American Mathe- matical Soc., 1978

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Limits of action convergent graph sequences with un- bounded (p, q)-norms, 2022

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Modeling Sparse Graph Sequences and Signals Using Generalized Graphons

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Convolutional neural networks for image classification

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation A.2.4 Marginal Measures When a measure is defined on a product space, it often represents a joint distribution of a sequence of random variables

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Intuitively (and informally), µx can be interpreted as a measure supported on the level set {w∈ Ω |f (w) = x}

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Observation 9e0fb859-ef6c-489c-b425-dae5722e7a3b · outbound

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A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Monte Carlo approximation

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Observation acba6d04-a8ad-4bd7-bcf0-0a8bf673ff9c · outbound

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Observation 0f2dce2b-2032-4446-9d88-a0470d8dc3ca · outbound

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Observation 921a7585-46c3-451a-a0e5-bc1a291051b1 · outbound

This paper cites neighborhoods.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation neighborhoods

Reference 74

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This paper cites Thediagonal marginalizationof ν, denoted by DMd(ν), is the Borel measure onR 2k obtained by marginalizing out the coordinatesy 2.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Thediagonal marginalizationof ν, denoted by DMd(ν), is the Borel measure onR 2k obtained by marginalizing out the coordinatesy 2

Reference 75

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Observation 255e56bd-c1eb-4678-b3b9-67020d0f43e4 · outbound

This paper cites Explicitly, DMd(Sk,d) := n DMd(ν) ν∈S Td k,d o.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation Explicitly, DMd(Sk,d) := n DMd(ν) ν∈S Td k,d o

Reference 76

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Observation cd4dac45-6335-4cad-93b4-e57252ad63bd · outbound

This paper cites graphing.

A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation graphing

Reference 77

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