In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and the edges by Jordan arcs (connected pieces of Jordan curves) joining the corresponding pairs of points. The points representing the vertices of a graph and the arcs representing its edges are called the vertices and the edges of the topological graph. It is usually assumed that any two edges of a topological graph cross a finite number of times, no edge passes through a vertex different from its endpoints, and no two edges touch each other (without crossing). A topological graph is also called a drawing of a graph. An important special class of topological graphs is the class of geometric graphs, wherethe edges are represented by line segments. (The term geometric graph is sometimes used in a broader, somewhat vague sense.) The theory of topological graphs is an area of graph theory, mainly concerned with combinatorial properties of topological graphs, in particular, with the crossing patterns of their edges. It is closely related to graph drawing, a field which is more application oriented, and topological graph theory, which focuses on embeddings of graphs in surfaces (that is, drawings without crossings). (Wikipedia).
From playlist 3d graphs
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
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Graph of x^2 + 6xb + 5b^2 as b varies
From playlist 3d graphs
From playlist 3d graphs
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
Graph of x^2 + 6xy + 5y^2 rotating
From playlist 3d graphs
From playlist 3d graphs
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
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
A formal definition of a Graph and its properties
From playlist Graph Theory