Oriented matroids | Extensions and generalizations of graphs | Matroid theory
In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. A signed graph is balanced if the product of edge signs around every cycle is positive. The name "signed graph" and the notion of balance appeared first in a mathematical paper of Frank Harary in 1953. Dénes Kőnig had already studied equivalent notions in 1936 under a different terminology but without recognizing the relevance of the sign group.At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs. Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in Σ. They have been applied to data classification in correlation clustering. (Wikipedia).
This video introduces signed graphs and signed graph theory. Signed graphs are graphs where the edges are given a positive or negative sign. They see applications in scheduling (signed graph coloring specifically), data science, social psychology, and more. In future videos we'll look at c
From playlist Summer of Math Exposition Youtube Videos
What is a Path Graph? | Graph Theory
What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can
From playlist Graph Theory
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Neural Networks, Session 1: Introduction to Graphs
Examples of Graph representation of data Motivation for doing machine learning on Graphs
From playlist Graph Neural Networks (Hands-on)
Shiping Liu (7/29/22): Signed graphs and Nodal domain theorems for symmetric matrices
Abstract: A signed graph is a graph whose edges are labelled by a signature. It serves as a simple model of discrete vector bundle. We will discuss nodal domain theorems for arbitrary symmetric matrices by exploring the induced signed graph structure. This is an extension of the nodal doma
From playlist Applied Geometry for Data Sciences 2022
Graph Neural Networks, Session 2: Graph Definition
Types of Graphs Common data structures for storing graphs
From playlist Graph Neural Networks (Hands-on)
What is a Graph? | Graph Theory
What is a graph? A graph theory graph, in particular, is the subject of discussion today. In graph theory, a graph is an ordered pair consisting of a vertex set, then an edge set. Graphs are often represented as diagrams, with dots representing vertices, and lines representing edges. Each
From playlist Graph Theory
A Few Conceptual Examples with Statistical Graphs
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A Few Conceptual Examples with Statistical Graphs
From playlist Statistics
Domino Tiling and Graph Theory
A beautiful solution to a difficult problem. Late pi day video! Code for the solution: https://github.com/vivek3141/domino-tiling Source Code for the animations: https://github.com/vivek3141/videos/blob/master/domino.py New website + store: https://vcubingx.com Permanent of a matrix: ht
From playlist Other Math Videos
Winnie Li: Towers of Ramanujan graphs
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Women at CIRM
X-Ramanujan graphs: ex uno plures - Ryan O'Donnell
Computer Science/Discrete Mathematics Seminar Topic: X-Ramanujan graphs: ex uno plures Speaker: Ryan O'Donnell Affiliation: Carnegie Mellon University Time/Room: 3:30pm - 4:30pm/Simonyi Hall 101 Date: October 29, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Ramanujan graphs of every degree - Daniel Spielman
Daniel Spielman Yale University November 6, 2014 We explain what Ramanujan graphs are, and prove that there exist infinite families of bipartite Ramanujan graphs of every degree. Our proof follows a plan suggested by Bilu and Linial, and exploits a proof of a conjecture of theirs about li
From playlist Mathematics
Calculus AB Homework 4.6: Relationship between f, f', and f''
Download Packet: https://goo.gl/tg9SDC ================================= AP Calculus AB / IB Math SL Unit 4: Applications of the Derivative Lesson 6: Relation between f, f', and f'' =================================
From playlist AP Calculus AB
Graphing Reflections of the Basic Rational Function f(x)=1/x
This video explains how to graph a reflection of f(x)=1/x about the x and y axes. http://mathispower4u.com
From playlist Graphing Rational Functions
Dimers, networks, and integrable systems - Anton Izosimov
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Dimers, networks, and integrable systems Speaker: Anton Izosimov Affiliation: The University of Arizona Date: March 18, 2022 I will review two combinatorial constructions of integrable systems: Goncharov-Keny
From playlist Mathematics
Introduction to Graph Transformations (Precalculus - College Algebra 14)
Support: https://www.patreon.com/ProfessorLeonard Cool Mathy Merch: https://professor-leonard.myshopify.com How to use Transformations to Graph basic functions and why the transformations do what they do.
From playlist Precalculus - College Algebra/Trigonometry
A formal definition of a Graph and its properties
From playlist Graph Theory