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Graph neural networks (GNNs) have recently grown in popularity in the field of artificial intelligence (AI) due to their unique ability to ingest relatively unstructured data types as input data. Although some elements of the GNN…
Artificial intelligence for graphs has achieved remarkable success in modeling complex systems, ranging from dynamic networks in biology to interacting particle systems in physics. However, the increasingly heterogeneous graph datasets call…
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…
In this note, I describe a formalism for treating knots as geometric spaces, and make an application to a simple statistical mechanics computation. The motivation for this study is the natural visual symmetry of the knot, and I describe how…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
Graph neural networks (GNNs) are powerful graph-based deep-learning models that have gained significant attention and demonstrated remarkable performance in various domains, including natural language processing, drug discovery, and…
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
The present paper is a review of the current state of Graph-Link Theory (graph-links are also closely related to homotopy classes of looped interlacement graphs), dealing with a generalisation of knots obtained by translating the…
Bidirected graphs are multigraphs where every edge has an independent direction at each end. In the paper, with an arbitrary bidirected graph we associate a non-negative integral quadratic form (called the incidence form of the graph), and…
We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
Unlabeled multigraphs have diverse applications across scientific fields, from transportation and social networks to polymer physics. In particular, multigraphs are essential for studying the relationship between the spatial organization…
Object segmentation is an important capability for robotic systems, in particular for grasping. We present a graph- based approach for the segmentation of simple objects from RGB-D images. We are interested in segmenting objects with large…
Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In…
This paper proposes a new method for converting a time-series into a weighted graph (complex network), which builds on the electrostatic conceptualization originating from physics. The proposed method conceptualizes a time-series as a…
A knot is an an embedding of a circle into three-dimensional space. We say that a knot is unknotted if there is an ambient isotopy of the embedding to a standard circle. By representing knots via planar diagrams, we discuss the problem of…
Objects and their relationships are critical contents for image understanding. A scene graph provides a structured description that captures these properties of an image. However, reasoning about the relationships between objects is very…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…