Related papers: Signed Graphs and Geometry
Let $G$ be a group. The directed endomorphism graph, $\dend(G)$ of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex $a$ to the vertex $b$ if $a \neq b$ and there exists an endomorphism on $G$ mapping…
We introduce a notion of a girth-regular graph as a $k$-regular graph for which there exists a non-descending sequence $(a_1, a_2, \dots, a_k)$ (called the signature) giving, for every vertex $u$ of the graph, the number of girth cycles the…
We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results…
I discuss the work of many authors on various matrices used to study signed graphs, concentrating on adjacency and incidence matrices and the closely related topics of Kirchhoff (`Laplacian') matrices, line graphs, and very strong…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
Let $G$ be a group. The directed endomorphism graph, \dend of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex `$a$' to the vertex `$\, b$' $(a \neq b) $ if and only if there exists an endomorphism on…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…
In this paper, we study the signed domination numbers of graphs and present new sharp lower and upper bounds for this parameter. As an example, we present a lower bound on signed domination number of trees in terms of the order, leaves and…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
Signed graphs are complex systems that represent trust relationships or preferences in various domains. Learning node representations in such graphs is crucial for many mining tasks. Although real-world signed relationships can be…
Many real-world relations can be represented by signed networks with positive and negative links, as a result of which signed network analysis has attracted increasing attention from multiple disciplines. With the increasing prevalence of…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
This paper surveys recent development of concepts related to coloring of signed graphs. Various approaches are presented and discussed.
Most modern theoretical considerations of the physical world suggest that nature is: (1) field-theoretic, (2) smooth, (3) local, (4) gauged, (5) containing fermions, and (6) non-perturbative. Tautologous as this may sound to experts, it is…
In this paper, we define several measures induced by a finite directed graph. The study themselves is interesting ont only in the noncommutative probability point of view but also in the algebraic structure point of view, since to define…