Related papers: Graph Lineages and Skeletal Graph Products
Graph neural networks (GNNs) are emerging for machine learning research on graph-structured data. GNNs achieve state-of-the-art performance on many tasks, but they face scalability challenges when it comes to real-world applications that…
Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers…
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,…
This work presents the use of graph learning for the prediction of multi-step experimental outcomes for applications across experimental research, including material science, chemistry, and biology. The viability of geometric learning for…
Most Graph Neural Networks (GNNs) cannot distinguish some graphs or indeed some pairs of nodes within a graph. This makes it impossible to solve certain classification tasks. However, adding additional node features to these models can…
A linear layout of a graph $ G $ consists of a linear order $\prec$ of the vertices and a partition of the edges. A part is called a queue (stack) if no two edges nest (cross), that is, two edges $ (v,w) $ and $ (x,y) $ with $ v \prec x…
Graph neural networks (GNNs) have emerged as a promising solution to deal with unstructured data, outperforming traditional deep learning architectures. However, most of the current GNN models are designed to work with a single graph, which…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Graphs are ubiquitous real-world data structures, and generative models that approximate distributions over graphs and derive new samples from them have significant importance. Among the known challenges in graph generation tasks,…
Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
This paper presents a novel framework for graded neural networks (GNNs) built over graded vector spaces $\V_\w^n$, extending classical neural architectures by incorporating algebraic grading. Leveraging a coordinate-wise grading structure…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…