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Graph neural networks (GNNs) have achieved state-of-the-art performance for node classification on graphs. The vast majority of existing works assume that genuine node labels are always provided for training. However, there has been very…

We present a case study in applied category theory written from the point of view of an applied domain: the formalization of the widely-used property graphs data model in an enterprise setting using elementary constructions from type theory…

Graph clustering has been popularly studied in recent years. However, most existing graph clustering methods focus on node-level clustering, i.e., grouping nodes in a single graph into clusters. In contrast, graph-level clustering, i.e.,…

String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…

Graphs with abundant attributes are essential in modeling interconnected entities and enhancing predictions across various real-world applications. Traditional Graph Neural Networks (GNNs) often require re-training for different graph tasks…

Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a…

Graph mining applications analyze the structural properties of large graphs, and they do so by finding subgraph isomorphisms, which makes them computationally intensive. Existing graph mining techniques including both custom graph mining…

Graphs provide a unified representation of semantic content and relational structure, making them a natural fit for domains such as molecular modeling, citation networks, and social graphs. Meanwhile, large language models (LLMs) have…

One of the emerging techniques in node classification in heterogeneous graphs is to restrict message aggregation to pre-defined, semantically meaningful structures called metapaths. This work is the first attempt to incorporate attention…

Graph-based methods have been demonstrated as one of the most effective approaches for semi-supervised learning, as they can exploit the connectivity patterns between labeled and unlabeled data samples to improve learning performance.…

We investigate the problem of producing structured graph representations of visual scenes. Our work analyzes the role of motifs: regularly appearing substructures in scene graphs. We present new quantitative insights on such repeated…

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition,…

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…

Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…

We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…

The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database…

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high…

In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…

Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…