Related papers: Incorporating Weisfeiler-Leman into algorithms for…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…