Graphon

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

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

Graph Theory: 02. Definition of a Graph

In this video we formally define what a graph is in Graph Theory and explain the concept with an example. In this introductory video, no previous knowledge of Graph Theory will be assumed. --An introduction to Graph Theory by Dr. Sarada Herke. This video is a remake of the "02. Definitio

From playlist Graph Theory part-1

Graphene Kirigami

Graphene is a one-atom thick 'supermaterial' with incredible strength and resilience. Kirigami is the ancient Japanese art of paper cutting. Combined, they could lead to a future of tiny mechanical parts and even mini machines... Find the full paper here: http://www.nature.com/doifinder/1

From playlist Technology

Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o

From playlist Graph Theory FAQs

The Definition of a Graph (Graph Theory)

The Definition of a Graph (Graph Theory) mathispower4u.com

From playlist Graph Theory (Discrete Math)

Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

Peter Caines: "Graphon MFGs: A Dynamical Equilibrium Theory for Large Populations on Large Scale..."

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Graphon Mean Field Games: A Dynamical Equilibrium Theory for Large Populations on Large Scale Networks" Peter Caines - McGill University Abstract: Very large scale (finite) networks (VLSNs) linkin

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

Joe Neeman - Large deviations for triangle densities

Recorded 10 February 2022. Joe Neeman of the University of Texas at Austin presents "Large deviations for triangle densities" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Borell's inequality characterizes the boolean-valued functions on Gaussian space th

From playlist Workshop: Calculus of Variations in Probability and Geometry

The Abel lectures: László Lovász and Avi Wigderson

0:30 Introduction by the Abel Prize Committee Chair, Hans Munthe-Kaas 02:42 László Lovász: Continuous limits of finite structures 49:27 Questions and answers 1:00:31 Avi Wigderson: The Value of Errors in Proofs 1:41:24 Questions and answers 1:50:20 Final remarks by John Grue, Chair of the

From playlist Abel Lectures

Graph Neural Networks, Session 2: Graph Definition

Types of Graphs Common data structures for storing graphs

From playlist Graph Neural Networks (Hands-on)

Shuangping Li (Princeton) -- Learning Sparse Graphons and the Generalized Kesten-Stigum Threshold

The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the

From playlist Northeastern Probability Seminar 2020

Graphon dynamics from population genetics by Siva Athreya

PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear

From playlist Advances in Applied Probability 2019

8ECM Abel Lecture: László Lovász

From playlist 𝙋𝙧𝙞𝙯𝙚 𝙇𝙚𝙘𝙩𝙪𝙧𝙚𝙨

Old and New Results on the Spread of the Spectrum of a Graph - John C Urschel

The spread of a matrix is defined as the diameter of its spectrum. This quantity has been well-studied for general matrices and has recently grown in popularity for the specific case of the adjacency matrix of a graph. Most notably, Gregory, Herkowitz, and Kirkland proved a number of key r

From playlist Mathematics

Christian Borgs: Graphons and graphexes as limits of sparse graphs - lecture 2

Abstract: Graphons and graphexes are limits of graphs which allow us to model and estimate properties of large-scale networks. In this pair of talks, we review the theory of dense graph limits, and give two alterative theories for limits of sparse graphs - one leading to unbounded graphons

From playlist Combinatorics

Subgraphs

A subgraph consist of nodes and edges of a larger graph. In this tutorial I show you what a subgraph is and present an elegant representation in Mathematica. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale an

From playlist Introducing graph theory

Jennifer Tour Chayes: Graphons and graphexes as limits of sparse graphs - lecture 1

Abstract: Graphons and graphexes are limits of graphs which allow us to model and estimate properties of large-scale networks. In this pair of talks, we review the theory of dense graph limits, and give two alterative theories for limits of sparse graphs - one leading to unbounded graphons

From playlist Combinatorics

Gauß Lecture in Leipzig 2022 | László Lovász - Discrete or Continuous

László Lovász, professor at Eötvös Loránd University and Alfréd Rényi Institute of Mathematics in Budapest, gave the distinguished Gauß lecture on the topic Discrete or Continuous?, the question of the continuous nature of our world from a mathematical perspective. This ceremonial event of

From playlist Various Lectures

Graphing Equations By Plotting Points - Part 1

This video shows how to graph equations by plotting points. Part 1 of 2 http://www.mathispower4u.yolasite.com

From playlist Graphing Various Functions