Related papers: Graph Lineages and Skeletal Graph Products

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

Complex networks can be used to analyze structures and systems in the embryo. Not only can we characterize growth and the emergence of form, but also differentiation. The process of differentiation from precursor cell populations to…

Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…

The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…

Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…

Graph neural networks (GNNs) are a class of deep models that operate on data with arbitrary topology represented as graphs. We introduce an efficient memory layer for GNNs that can jointly learn node representations and coarsen the graph.…

With the advances of data-driven machine learning research, a wide variety of prediction problems have been tackled. It has become critical to explore how machine learning and specifically deep learning methods can be exploited to analyse…

A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear…

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…

Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…

We define graded group schemes and graded group varieties and develop their theory. Graded group schemes are the graded analogue of group schemes and are in correspondence with graded Hopf algebra. In this setting, graded group varieties…

Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark…

Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

The era of data deluge has sparked the interest in graph-based learning methods in a number of disciplines such as sociology, biology, neuroscience, or engineering. In this paper, we introduce a graph recurrent neural network (GRNN) for…

Graph neural networks, a powerful deep learning tool to model graph-structured data, have demonstrated remarkable performance on numerous graph learning tasks. To address the data noise and data scarcity issues in deep graph learning, the…

Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…

Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…