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
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
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
A formal definition of a Graph and its properties
From playlist Graph Theory
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
Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
Classical and Digital Topological Groups
A research talk presented at the Fairfield University Mathematics Research Seminar, October 6, 2022. Should be accessible to a general mathematics audience, combining ideas from topology, graph theory, and abstract algebra. The paper is by me and Dae Woong Lee, available here: https://arx
From playlist Research & conference talks
Topological Sort | Kahn's Algorithm | Graph Theory
Source code repository: https://github.com/williamfiset/algorithms#graph-theory Video slides: https://github.com/williamfiset/algorithms/tree/master/slides Website: http://www.williamfiset.com Audio intro/outro composed by Richard Saney (rnsaney@gmail.com) 0:00 Intro 0:22 Topological s
From playlist Graph Theory Playlist
Breakdown of the basic components of graphs in graph theory
From playlist Graph Theory
Yuzhou Chen (10/27/21): Topological Relational Learning on Graphs
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framewo
From playlist AATRN 2021
NEW TOPOLOGICAL LAYER in Graph Neural Networks (GCN), Filtrations, Persistent Homology - ICLR 2022
NEW: integrate a topological layer as one of the Graph Convolutional Network (GCN) layer in to your GCN to obtain essential topological info about the Graph. Persistent Homology, Learnable Filtrations and Topology. Topological Data Analysis (TDA). Although this method is limited to l=1, c
From playlist Learn Graph Neural Networks: code, examples and theory
Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs
Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob
From playlist TDA: Tutte Institute & Western University - 2021
CSE373 2012 - Lecture 14 - Graph Algorithms (con't)
This is Lecture 14 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2012.
From playlist CSE373 - Analysis of Algorithms - 2012 SBU
Topological similarity of random cell complexes, and applications - Benjamin Schweinhart
Benjamin Schweinhart Princeton University December 10, 2014 Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth',
From playlist Mathematics
Topological Message Passing on GNN | SIMPLICIAL COMPLEXES on CW Networks #ai
We go from Message Passing GNN (MPGNN) to TOPOLOGICAL Message Passing on CW Networks: Lifting a Graph to a higher topological space allows for high-dimensional interactions (greater than 2) given our higher-dim topological spaces. Computational Graph Neural Networks increase its complexiti
From playlist Learn Graph Neural Networks: code, examples and theory
The role of topology and compactness (...) - CEB T2 2017 - Varadhan - 3/3
S.R.S. Varadhan (Courant Institute) - 09/06/2017 The role of topology and compactness in the theory of large deviations When a large deviation result is proved there is some topology involved in the statement because it affects the class of sets for which the estimates hold. Often the cho
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Topological Sort Algorithm | Graph Theory
How to find the topological sort of a directed acyclic graph Shortest path on a Directed Acyclic Graph (DAG): https://www.youtube.com/watch?v=TXkDpqjDMHA Github source code link: https://github.com/williamfiset/algorithms#graph-theory 0:00 Intro 0:18 Topological sort real life examples
From playlist Graph Theory Playlist
Section 4b: Graph Connectivity
From playlist Graph Theory