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Graph Neural Networks (GNNs) are learning models aimed at processing graphs and signals on graphs. The most popular and successful GNNs are based on message passing schemes. Such schemes inherently have limited expressive power when it…

Machine Learning · Computer Science 2022-06-24 Jacob Bamberger

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in…

Computational Complexity · Computer Science 2017-05-10 Daniel Neuen , Pascal Schweitzer

In these lecture notes, we first recall the connection between graph neural networks, Weisfeiler-Lehman tests and logics such as first-order logic and graded modal logic. We then present a modal logic in which counting modalities appear in…

Logic in Computer Science · Computer Science 2025-10-14 François Schwarzentruber

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph…

Social and Information Networks · Computer Science 2018-04-11 William L. Hamilton , Rex Ying , Jure Leskovec

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

Machine Learning · Statistics 2020-06-25 Soumyasundar Pal , Saber Malekmohammadi , Florence Regol , Yingxue Zhang , Yishi Xu , Mark Coates

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

Combinatorics · Mathematics 2023-06-06 Kai Siong Yow , Ningyi Liao , Siqiang Luo , Reynold Cheng , Chenhao Ma , Xiaolin Han

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for…

Machine Learning · Computer Science 2023-05-31 Christopher Morris , Floris Geerts , Jan Tönshoff , Martin Grohe

The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…

Machine Learning · Computer Science 2021-10-25 Till Hendrik Schulz , Pascal Welke , Stefan Wrobel

In recent years, Graph Neural Network (GNN) has bloomly progressed for its power in processing graph-based data. Most GNNs follow a message passing scheme, and their expressive power is mathematically limited by the discriminative ability…

Machine Learning · Computer Science 2021-04-06 Alan J. X. Guo , Qing-Hu Hou , Ou Wu

The invariance to permutations of the adjacency matrix, i.e., graph isomorphism, is an overarching requirement for Graph Neural Networks (GNNs). Conventionally, this prerequisite can be satisfied by the invariant operations over node…

Machine Learning · Computer Science 2022-05-31 Zhongyu Huang , Yingheng Wang , Chaozhuo Li , Huiguang He

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

Machine Learning · Computer Science 2022-03-18 Max Horn , Edward De Brouwer , Michael Moor , Yves Moreau , Bastian Rieck , Karsten Borgwardt

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

Machine Learning · Computer Science 2024-01-17 Sanaz Hasanzadeh Fard

Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…

Machine Learning · Computer Science 2022-11-07 Falih Gozi Febrinanto , Feng Xia , Kristen Moore , Chandra Thapa , Charu Aggarwal

The $k$-dimensional Weisfeiler-Leman algorithm is a powerful tool in graph isomorphism testing. For an input graph $G$, the algorithm determines a canonical coloring of $s$-tuples of vertices of $G$ for each $s$ between 1 and $k$. We say…

Computational Complexity · Computer Science 2020-05-20 Frank Fuhlbrück , Johannes Köbler , Oleg Verbitsky

In recent years there has been a rapid increase in classification methods on graph structured data. Both in graph kernels and graph neural networks, one of the implicit assumptions of successful state-of-the-art models was that…

Machine Learning · Computer Science 2019-11-01 Sergei Ivanov , Sergei Sviridov , Evgeny Burnaev

We provide a criterion to distinguish two graphs which are indistinguishable by $2$-dimensional Weisfeiler-Lehman algorithm for almost all graphs. Haemers conjectured that almost all graphs are identified by their spectrum. Our approach…

Combinatorics · Mathematics 2025-11-21 Wei Wang , Da Zhao

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…

Machine Learning · Computer Science 2021-05-04 Feng Xia , Ke Sun , Shuo Yu , Abdul Aziz , Liangtian Wan , Shirui Pan , Huan Liu

Message passing graph neural networks (GNNs) are known to have their expressiveness upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) algorithm. To achieve more powerful GNNs, existing attempts either require ad hoc features, or…

Machine Learning · Computer Science 2024-01-24 Meng Liu , Haiyang Yu , Shuiwang Ji

In this paper, we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the Weisfeiler-Leman…

Data Structures and Algorithms · Computer Science 2018-05-23 Holger Dell , Martin Grohe , Gaurav Rattan

Graph Neural Networks (GNNs) have emerged as prominent models for representation learning on graph structured data. GNNs follow an approach of message passing analogous to 1-dimensional Weisfeiler Lehman (1-WL) test for graph isomorphism…

Machine Learning · Computer Science 2022-03-18 Mohammed Haroon Dupty , Wee Sun Lee