Related papers: Hypergraph Isomorphism Computation
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…
A hypergraph consists of a set of nodes along with a collection of subsets of the nodes called hyperedges. Higher-order link prediction is the task of predicting the existence of a missing hyperedge in a hypergraph. A hyperedge…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…
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…
Aligning users across networks using graph representation learning has been found effective where the alignment is accomplished in a low-dimensional embedding space. Yet, achieving highly precise alignment is still challenging, especially…
The Weisfeiler-Leman algorithm ($1$-WL) is a well-studied heuristic for the graph isomorphism problem. Recently, the algorithm has played a prominent role in understanding the expressive power of message-passing graph neural networks…
Given a pair of graphs $\textbf{A}$ and $\textbf{B}$, the problems of deciding whether there exists either a homomorphism or an isomorphism from $\textbf{A}$ to $\textbf{B}$ have received a lot of attention. While graph homomorphism is…
The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many…
In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we…
The graphlet kernel is a classical method in graph classification. It however suffers from a high computation cost due to the isomorphism test it includes. As a generic proxy, and in general at the cost of losing some information, this test…
Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…
While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes…
In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically --…
The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a fruitful approach to the Graph Isomorphism problem. 2-WL corresponds to the original algorithm suggested by Weisfeiler and Leman over 50 years ago. 1-WL is the classical color…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
The Weisfeiler-Leman (WL) algorithm is a combinatorial procedure that computes colorings on graphs, which can often be used to detect their (non-)isomorphism. Particularly the 1- and 2-dimensional versions 1-WL and 2-WL have received much…
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…