Related papers: Resolving Node Identifiability in Graph Neural Pro…

Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good…

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…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly,…

The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…

Combining the message-passing paradigm with the global attention mechanism has emerged as an effective framework for learning over graphs. The message-passing paradigm and the global attention mechanism fundamentally generate node…

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the…

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their…

Recently, Transformers for graph representation learning have become increasingly popular, achieving state-of-the-art performance on a wide-variety of graph datasets, either alone or in combination with message-passing graph neural networks…

Positional Encodings (PEs) are essential for injecting structural information into Graph Neural Networks (GNNs), particularly Graph Transformers, yet their empirical impact remains insufficiently understood. We introduce a unified…

In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection…

Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A…

The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which…

The expressive power of message passing GNNs is upper-bounded by Weisfeiler-Lehman (WL) test. To achieve high expressive GNNs beyond WL test, we propose a novel graph isomorphism test method, namely Twin-WL, which simultaneously passes node…

The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…

We present a novel approach for graph classification based on tabularizing graph data via new variants of the Weisfeiler-Leman algorithm and then applying methods for tabular data. The variants are obtained by modifying the underlying…

This paper presents the Persistent Weisfeiler-Lehman Random walk scheme (abbreviated as PWLR) for graph representations, a novel mathematical framework which produces a collection of explainable low-dimensional representations of graphs…

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…

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…