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Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

Universal graph pre-training has emerged as a key paradigm in graph representation learning, offering a promising way to train encoders to learn transferable representations from unlabeled graphs and to effectively generalize across a wide…

A Gelfand model for a semisimple algebra A over C is a complex linear representation that contains each irreducible representation of A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a…

We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…

We propose a novel database model whose basic structure is a labeled, directed, acyclic graph with a single root, in which the nodes represent the data sets of an application and the edges represent functional relationships among the data…

In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…

The discovery and analysis of network patterns are central to the scientific enterprise. In the present work, we developed and evaluated a new approach that learns the building blocks of graphs that can be used to understand and generate…

Large language models (LLMs) are being increasingly explored for graph tasks. Despite their remarkable success in text-based tasks, LLMs' capabilities in understanding explicit graph structures remain limited, particularly with large…

We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…

Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…

In this paper, we study semi-supervised graph classification, which aims at accurately predicting the categories of graphs in scenarios with limited labeled graphs and abundant unlabeled graphs. Despite the promising capability of graph…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

-Background. Network neuroscience examines the brain as a complex system represented by a network (or connectome), providing deeper insights into the brain morphology and function, allowing the identification of atypical brain connectivity…

Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, e.g. graph convolutional networks (GCN) and graph attention networks (GAT), adequately utilize…

Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…

The emergence of graph neural networks (GNNs) has offered a powerful tool for semi-supervised node classification tasks. Subsequent studies have achieved further improvements through refining the message passing schemes in GNN models or…

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…

Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the…