Graph connectivity | Graph theory objects
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the whole graph. Components are sometimes called connected components. The number of components in a given graph is an important graph invariant, and is closely related to invariants of matroids, topological spaces, and matrices. In random graphs, a frequently occurring phenomenon is the incidence of a giant component, one component that is significantly larger than the others; and of a percolation threshold, an edge probability above which a giant component exists and below which it does not. The components of a graph can be constructed in linear time, and a special case of the problem, connected-component labeling, is a basic technique in image analysis. Dynamic connectivity algorithms maintain components as edges are inserted or deleted in a graph, in low time per change. In computational complexity theory, connected components have been used to study algorithms with limited space complexity, and sublinear time algorithms can accurately estimate the number of components. (Wikipedia).
Explaining Components of Graphs | Graph Theory
What are components of graphs? We'll be defining connected components in graph theory in today's lesson, with examples of components as well! Check out my previous lesson explaining components: https://www.youtube.com/watch?v=q6pKCP1W0dk A component of a graph is a maximal connected subg
From playlist Graph Theory
What is a Component of a Graph? | Connected Components, Graph Theory
What is a component of a graph? Sometimes called connected components, some graphs have very distinct pieces that have no paths between each other, these 'pieces' or subgraphs, are called components, and we go over the definition of component in today's graph theory video lesson! A compon
From playlist Graph Theory
Graphs Have at Least n-m Components | Graph Theory
A graph with n vertices and m edges has at least n-m components. We justify this claim in today's graph theory lesson. Imagine a graph with its n vertices and without any edges. This graph would have n components, each vertex is a trivial subgraph. Then, each additional edge could join at
From playlist Graph Theory
Breakdown of the basic components of graphs in graph theory
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
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
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 Theory: 04. Families of Graphs
This video describes some important families of graph in Graph Theory, including Complete Graphs, Bipartite Graphs, Paths and Cycles. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https://www.youtube.com/watch?v=S1Zwhz-MhCs (Graph Theory: 02. Definit
From playlist Graph Theory part-1
Edge Subtraction and Bridges in Graphs | Graph Theory, Edge Deletion
What is edge subtraction in graph theory? How do we delete an edge from a graph? And what is a bridge? That's what we'll be going over in today's video graph theory lesson! When we delete a vertex from a graph we also need to delete the incident edges, but deleting an edge is a bit simple
From playlist Graph Theory
Subtracting a Vertex from a Graph (Vertex Deletion) | Graph Theory
How do we subtract a vertex from a graph? This is also sometimes referred to as deleting a vertex from a graph. So call it vertex subtraction or vertex deletion, whichever you please, that’s what we are going over today! Deleting a vertex from a graph is pretty intuitive. First we just re
From playlist Graph Theory
Depth First Search Algorithm | Graph Theory
Depth First Search (DFS) algorithm explanation Source code: https://github.com/williamfiset/algorithms#graph-theory Video Slides: https://github.com/williamfiset/Algorithms/tree/master/slides/graphtheory 0:00 Depth first search as an algorithm template 1:04 Simple DFS example 3:30 Depth
From playlist Graph Theory Playlist
Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions
What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree
From playlist Graph Theory
Overview of algorithms in Graph Theory
An overview of the computer science algorithms in Graph Theory Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-theory-algorithms Previous video (intro): h
From playlist Graph Theory Playlist
Introduction to Graph Theory: A Computer Science Perspective
In this video, I introduce the field of graph theory. We first answer the important question of why someone should even care about studying graph theory through an application perspective. Afterwards, we introduce definitions and essential terminology in graph theory, followed by a discuss
From playlist Graph Theory
Graph Theory: 31. Lemma on Hamiltonian Graphs
I explain a proof of the following lemma: If a graph G is Hamiltonian, then for every nonempty subset S of the vertices, the number of connected components of the graph G-S is at most the size of S. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/3xeYc
From playlist Graph Theory part-6
What are Vertex Separating Sets? | Graph Theory
What are vertex separating sets in graph theory? We'll be going over the definition of a vertex separating set and some examples in today's video graph theory lesson! Let G be a graph and S be a vertex cut of G. As in, S is a set of vertices of G such that G - S is disconnected. Then, let
From playlist Set Theory
From playlist Contributed talks One World Symposium 2020
From playlist M. Graph Theory