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Characterizing the separation power of graph neural networks (GNNs) provides an understanding of their limitations for graph learning tasks. Results regarding separation power are, however, usually geared at specific GNN architectures, and…

Machine Learning · Computer Science 2022-04-12 Floris Geerts , Juan L. Reutter

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their…

Machine Learning · Computer Science 2021-06-15 Muhammet Balcilar , Pierre Héroux , Benoit Gaüzère , Pascal Vasseur , Sébastien Adam , Paul Honeine

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the $k$-dimensional Weisfeiler-Leman ($k$WL) test, a widely-recognized method for verifying…

Machine Learning · Computer Science 2024-03-29 Matthias Lanzinger , Pablo Barceló

The color refinement algorithm is mainly known as a heuristic method for graph isomorphism testing. It has surprising but natural characterizations in terms of, for example, homomorphism counts from trees and solutions to a system of linear…

Combinatorics · Mathematics 2023-12-20 Jan Böker

The expressive power of message passing GNNs is upper-bounded by Weisfeiler-Lehman (WL) test. To achieve high expressive GNNs beyond WL test, we propose a novel graph isomorphism test method, namely Twin-WL, which simultaneously passes node…

Machine Learning · Computer Science 2022-03-23 Zhaohui Wang , Qi Cao , Huawei Shen , Bingbing Xu , Xueqi Cheng

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are…

Machine Learning · Computer Science 2023-06-12 Gaspard Michel , Giannis Nikolentzos , Johannes Lutzeyer , Michalis Vazirgiannis

Graph neural network architectures aligned with the $k$-dimensional Weisfeiler--Leman ($k$-WL) hierarchy offer theoretically well-understood expressive power. However, these architectures often fail to deliver state-of-the-art predictive…

Machine Learning · Computer Science 2024-06-06 Luis Müller , Christopher Morris

Message passing Graph Neural Networks (GNNs) provide a powerful modeling framework for relational data. However, the expressive power of existing GNNs is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test, which means…

Machine Learning · Computer Science 2021-02-08 Jiaxuan You , Jonathan Gomes-Selman , Rex Ying , Jure Leskovec

The expressive power of Graph Neural Networks (GNNs) is often analysed via correspondence to the Weisfeiler-Leman (WL) algorithm and fragments of first-order logic. Standard GNNs are limited to performing aggregation over immediate…

Machine Learning · Computer Science 2026-02-23 Huan Luo , Jonni Virtema

Subgraph counting is a fundamental task for analyzing structural patterns in graph-structured data, with important applications in domains such as computational biology and social network analysis, where recurring motifs reveal functional…

Machine Learning · Computer Science 2025-12-02 Shubhajit Roy , Shrutimoy Das , Binita Maity , Anant Kumar , Anirban Dasgupta

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive…

Machine Learning · Computer Science 2021-06-15 Cristian Bodnar , Fabrizio Frasca , Yu Guang Wang , Nina Otter , Guido Montúfar , Pietro Liò , Michael Bronstein

Graph neural networks (GNNs) have become the \textit{de facto} standard for representational learning in graphs, and have achieved state-of-the-art performance in many graph-related tasks; however, it has been shown that the expressive…

Machine Learning · Computer Science 2024-06-28 Tianjun Yao , Yiongxu Wang , Kun Zhang , Shangsong Liang

We propose a Graph Neural Network with greater expressive power than commonly used GNNs - not constrained to only differentiate between graphs that Weisfeiler-Lehman test recognizes to be non-isomorphic. We use a graph attention network…

Machine Learning · Computer Science 2020-04-14 Stanisław Purgał

The Weisfeiler-Leman (WL) algorithm is a well-known combinatorial procedure for detecting symmetries in graphs and it is widely used in graph-isomorphism tests. It proceeds by iteratively refining a colouring of vertex tuples. The number of…

Discrete Mathematics · Computer Science 2021-07-01 Martin Grohe , Sandra Kiefer

Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the…

Machine Learning · Computer Science 2022-03-03 Or Feldman , Amit Boyarski , Shai Feldman , Dani Kogan , Avi Mendelson , Chaim Baskin

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection…

Machine Learning · Computer Science 2023-03-01 Giannis Nikolentzos , Michail Chatzianastasis , Michalis Vazirgiannis

Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be…

Subgraph representation learning has been effective in solving various real-world problems. However, current graph neural networks (GNNs) produce suboptimal results for subgraph-level tasks due to their inability to capture complex…

Machine Learning · Computer Science 2025-11-12 Dongkwan Kim , Alice Oh

The Weisfeiler-Leman (WL) dimension is an established measure for the inherent descriptive complexity of graphs and relational structures. It corresponds to the number of variables that are needed and sufficient to define the object of…

Discrete Mathematics · Computer Science 2024-02-06 Sandra Kiefer , Daniel Neuen

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful…