Related papers: CelticGraph: Drawing Graphs as Celtic Knots and Li…

Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…

Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…

A graph is said to be a segment graph if its vertices can be mapped to line segments in the plane such that two vertices have an edge between them if and only if their corresponding line segments intersect. Kratochv\'{i}l and Kub\v{e}na…

Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and in which each edge $(u,v)$ is represented…

Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…

We describe a method of encoding various types of link diagrams, including those with classical, flat, rigid, welded, and virtual crossings. We show that this method may be used to encode link diagrams, up to equivalence, in a notation…

In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…

Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually…

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

Trace diagrams are structured graphs with edges labeled by matrices. Each diagram has an interpretation as a particular multilinear function. We provide a rigorous combinatorial definition of these diagrams using a notion of signed graph…

A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding…

Cactus doodles are combinatorial/geometric objects that are related to cactus groups in the same way as knots are related to braids. We define them in terms of local moves on plane curves, show that they can be obtained from elements of the…

This paper introduces the concept of a Fourier knot. A Fourier knot is a knot that is represented by a parametrized curve in three dimensional space such that the coordinate functions are finite Fourier series in the parameter. The…

Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…

This paper is devoted to qualgebras and squandles, which are quandles enriched with a compatible binary/unary operation. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. Topologically,…

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Mosaic diagrams for knots were first introduced in 2008 by Lomanoco and Kauffman for the purpose of building a quantum knot system. Since then, many others have explored the structure of these knot mosaic diagrams, as they are interesting…