Related papers: Line graphs e contrazioni: un approccio rigoroso a…
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
By defining grids as graphs, geometric graphs can be represented in a very concise way.
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with…
Selecting a subset of cells is a common task in data engineering, for example, to remove errors or select only specific parts of a table. Multiple approaches to express this selection exist. One option is numeric indexing, commonly found in…
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.
In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main…
Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…
The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the…
We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.
The notion of term graph encodes a refinement of inductively generated syntax in which regard is paid to the the sharing and discard of subterms. Inductively generated syntax has an abstract expression in terms of initial algebras for…
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…
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…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…
In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. Unlike for undirected graphs, some ends are joined by limit…
In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…