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The expressive power of graph neural network formalisms is commonly measured by their ability to distinguish graphs.
An optimal lower bound on the number of variables for graph identifications
Jin-Yi Cai, Martin Fürer, and Neil Immerman · 1992
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Can graph neural networks count substructures?
Zhengdao Chen, Lei Chen, Soledad Villar, and Joan Bruna · 2002
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Random features strengthen graph neural networks
Ryoma Sato, Makoto Yamada, and Hisashi Kashima · 2002
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A survey on the expressive power of graph neural networks
Ryoma Sato · 2003
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Let’s agree to degree: Comparing graph convolutional networks in the message-passing framework
Floris Geerts, Filip Mazowiecki, and Guillermo A Pérez · 2004
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Graph homomorphism convolution
Hoang NT and Takanori Maehara · 2005
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Characterizing the expressive power of invariant and equivariant graph neural networks
Waïss Azizian and Marc Lelarge · 2006
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Walk message passing neural networks and second-order graph neural networks
Floris Geerts · 2006
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The graph neural network model
Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini · 2008
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Pebble games and linear equations
Martin Grohe and Martin Otto · 2015
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On the combinatorial power of the Weisfeiler-Lehman algorithm
Martin Fürer · 2017
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Neural message passing for quantum chemistry
Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl · 2017
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Descriptive Complexity, Canonisation, and Definable Graph Structure Theory
Martin Grohe · 2017
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Semi-supervised classification with graph convolutional networks
Thomas N. Kipf and Max Welling · 2017
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Lovász meets Weisfeiler and Leman
Holger Dell, Martin Grohe, and Gaurav Rattan · 2018
Cited alongside, same era.
Open problems: Approximation power of invariant graph networks
Haggai Maron, Heli Ben-Hamu, and Yaron Lipman · 2019
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Weisfeiler and Leman go neural: Higher-order graph neural networks
Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe · 2019
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Approximation ratios of graph neural networks for combinatorial problems
Ryoma Sato, Makoto Yamada, and Hisashi Kashima · 2019
Later among the works it cites.
How powerful are graph neural networks?
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka · 2019
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On Weisfeiler-Leman invariance: Subgraph counts and related graph properties
V. Arvind, Frank Fuhlbrück, Johannes Köbler, and Oleg Verbitsky · 2020
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The logical expressiveness of graph neural networks
Pablo Barceló, Egor V Kostylev, Mikael Monet, Jorge Pérez, Juan Reutter, and Juan Pablo Silva · 2020
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Covariant compositional networks for learning graphs
Risi Kondor, Hy Truong Son, Horace Pan, Brandon Anderson, and Shubhendu Trivedi · 2018
Cited alongside, same era.
On the expressive power of linear algebra on graphs
Floris Geerts · 2019
Cited alongside, same era.
Walk refinement, walk logic, and the iteration number of the Weisfeiler-Leman algorithm
Moritz Lichter, Ilia Ponomarenko, and Pascal Schweitzer · 2019
Cited alongside, same era.
Provably powerful graph networks
Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman
Cited in the paper.
Invariant and equivariant graph networks
Haggai Maron, Heli Ben-Hamu, Nadav Shamir, and Yaron Lipman
Cited in the paper.
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word2vec, node2vec, graph2vec, x2vec: Towards a theory of vector embeddings of structured data
Martin Grohe · 2020
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What graph neural networks cannot learn: depth vs width
Andreas Loukas · 2020
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