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Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to…
Knowledge in materials science is widely dispersed across extensive scientific literature, posing significant challenges to the efficient discovery and integration of new materials. Traditional methods, often reliant on costly and…
Large language models (LLMs) have demonstrated immense potential across various tasks. However, research for exploring and improving the capabilities of LLMs in interpreting graph structures remains limited. To address this gap, we conduct…
Graph Neural Networks (GNNs) have evolved to understand graph structures through recursive exchanges and aggregations among nodes. To enhance robustness, self-supervised learning (SSL) has become a vital tool for data augmentation.…
Recent work at the intersection of formal language theory and graph theory has explored graph grammars for graph modeling. However, existing models and formalisms can only operate on homogeneous (i.e., untyped or unattributed) graphs. We…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…
Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
The complicated syntax structure of natural language is hard to be explicitly modeled by sequence-based models. Graph is a natural structure to describe the complicated relation between tokens. The recent advance in Graph Neural Networks…
Graphs can model complicated interactions between entities, which naturally emerge in many important applications. These applications can often be cast into standard graph learning tasks, in which a crucial step is to learn low-dimensional…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
While large language models (LLMs) have made considerable advancements in understanding and generating unstructured text, their application in structured data remains underexplored. Particularly, using LLMs for complex reasoning tasks on…
We consider three important and well-studied algorithmic problems in group theory: the word, geodesic, and conjugacy problem. We show transfer results from individual groups to graph products. We concentrate on logspace complexity because…
Graph neural networks (GNNs) have recently emerged as a dominant paradigm for machine learning with graphs. Research on GNNs has mainly focused on the family of message passing neural networks (MPNNs). Similar to the Weisfeiler-Leman (WL)…
Graph-theoretic problems arise in real-world applications like logistics, communication networks, and traffic optimization. These problems are often complex, noisy, and irregular, posing challenges for traditional algorithms. Large language…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be thought of as being a kind of discrete Laplacian, and we first discuss…
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…