Related papers: Signed Graphs and Geometry
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…
Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions,…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating…
A signed graph is a graph whose edges are labelled positive or negative. The sign of a circle (cycle, circuit) is the product of the signs of its edges. Most of the essential properties of a signed graph depend on the signs of its circles.…
A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks,…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
We define a special sort of weighted oriented graphs, signed quivers. Each of these yields a symmetric quiver, i.e., a quiver endowed with an involutive anti-automorphism and the inherited signs. We develop a representation theory of…
A mixed graph is a graph with some directed edges and some undirected edges. We introduce the notion of mixed matroids as a generalization of mixed graphs. A mixed matroid can be viewed as an oriented matroid in which the signs over a fixed…
A signed graph is a graph whose edges are signed. In a vertex-signed graph the vertices are signed. The latter is called consistent if the product of signs in every circle is positive. The line graph of a signed graph is naturally…
Signed graphs are studied since the middle of the last century. Recently, the notion of homomorphism of signed graphs has been introduced since this notion captures a number of well known conjectures which can be reformulated using the…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
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…
These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
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…