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Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly…

Rings and Algebras · Mathematics 2025-09-18 Lisa Orloff Clark , Malcolm Jones

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

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

Discrete Mathematics · Computer Science 2014-11-10 Pascal Schweitzer

Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator…

Machine Learning · Computer Science 2020-09-22 Clemens Damke , Vitalik Melnikov , Eyke Hüllermeier

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

The stabilization algorithm of Weisfeiler and Leman has as an input any square matrix A of order n and returns the minimal cellular (coherent) algebra W(A) which includes A. In case when A=A(G) is the adjacency matrix of a graph G the…

Combinatorics · Mathematics 2010-02-10 Luitpold Babel , Irina V. Chuvaeva , Mikhail Klin , Dmitrii V. Pasechnik

There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…

Combinatorics · Mathematics 2025-10-17 Michael Anastos , Matthew Kwan , Benjamin Moore

Low-pass graph filters are fundamental for signal processing on graphs and other non-Euclidean domains. However, the computation of such filters for parametric graph families can be prohibitively expensive as computation of the…

Machine Learning · Computer Science 2025-10-28 Anton Savostianov , Michael T. Schaub , Benjamin Stamm

Graph neural networks have been widely used on modeling graph data, achieving impressive results on node classification and link prediction tasks. Yet, obtaining an accurate representation for a graph further requires a pooling function…

Machine Learning · Computer Science 2021-06-29 Jinheon Baek , Minki Kang , Sung Ju Hwang

The $k$-dimensional Weisfeiler-Leman procedure ($k$-WL), which colors $k$-tuples of vertices in rounds based on the neighborhood structure in the graph, has proven to be immensely fruitful in the algorithmic study of Graph Isomorphism. More…

Computational Complexity · Computer Science 2020-06-08 V. Arvind , Frank Fuhlbrück , Johannes Köbler , Oleg Verbitsky

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the…

Machine Learning · Computer Science 2025-12-12 Lin Du , Lu Bai , Jincheng Li , Lixin Cui , Hangyuan Du , Lichi Zhang , Yuting Chen , Zhao Li

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…

Discrete Mathematics · Computer Science 2014-03-31 Yota Otachi , Pascal Schweitzer

We focus on graph classification using a graph neural network (GNN) model that precomputes the node features using a bank of neighborhood aggregation graph operators arranged in parallel. These GNN models have a natural advantage of reduced…

Machine Learning · Computer Science 2022-11-23 Siddhant Doshi , Sundeep Prabhakar Chepuri

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

Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…

Combinatorics · Mathematics 2024-08-27 Rui Xue

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

We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL), which allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. We prove that, as an…

Logic in Computer Science · Computer Science 2020-03-25 Martin Grohe , Pascal Schweitzer , Daniel Wiebking

The ability of graph neural networks (GNNs) to count homomorphisms has recently been proposed as a practical and fine-grained measure of their expressive power. Although several existing works have investigated the homomorphism counting…

Machine Learning · Computer Science 2024-10-07 Junru Zhou , Muhan Zhang

We propose a general multi-class visual recognition model, termed the Classifier Graph, which aims to generalize and integrate ideas from many of today's successful hierarchical recognition approaches. Our graph-based model has the…

Computer Vision and Pattern Recognition · Computer Science 2014-04-11 Marius Leordeanu , Rahul Sukthankar

While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…

Machine Learning · Computer Science 2023-09-26 Giorgos Bouritsas , Fabrizio Frasca , Stefanos Zafeiriou , Michael M. Bronstein