Related papers: Graph Filtration Kernels

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…

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…

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…

Label propagation is a powerful and flexible semi-supervised learning technique on graphs. Neural networks, on the other hand, have proven track records in many supervised learning tasks. In this work, we propose a training framework with a…

Graph Neural Networks (GNNs) have achieved remarkable success in various graph-based learning tasks. While their performance is often attributed to the powerful neighborhood aggregation mechanism, recent studies suggest that other…

In this paper we cast neural networks defined on graphs as message-passing neural networks (MPNNs) in order to study the distinguishing power of different classes of such models. We are interested in whether certain architectures are able…

Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…

In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

We precisely characterize the expressivity of computable Recurrent Graph Neural Networks (recurrent GNNs). We prove that recurrent GNNs with finite-precision parameters, sum aggregation, and ReLU activation, can compute any graph algorithm…

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 Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a…

This paper studies semi-supervised graph classification, which is an important problem with various applications in social network analysis and bioinformatics. This problem is typically solved by using graph neural networks (GNNs), which…

The expressive power of graph neural networks (GNNs) is typically understood through their correspondence with graph isomorphism tests such as the Weisfeiler-Leman (WL) hierarchy. While more expressive GNNs can distinguish a richer set of…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

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…

Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…

Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the…

The design of neural architectures for structured objects is typically guided by experimental insights rather than a formal process. In this work, we appeal to kernels over combinatorial structures, such as sequences and graphs, to derive…

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…