Graph connectivity | Graph families

Biconnected graph

In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected graph has no articulation vertices. The property of being 2-connected is equivalent to biconnectivity, except that the complete graph of two vertices is usually not regarded as 2-connected. This property is especially useful in maintaining a graph with a two-fold redundancy, to prevent disconnection upon the removal of a single edge (or connection). The use of biconnected graphs is very important in the field of networking (see Network flow), because of this property of redundancy. (Wikipedia).

Biconnected graph
Video thumbnail

What is a Bipartite Graph? | Graph Theory

What is a bipartite graph? We go over it in today’s lesson! I find all of these different types of graphs very interesting, so I hope you will enjoy this lesson. A bipartite graph is any graph whose vertex set can be partitioned into two disjoint sets (called partite sets), such that all e

From playlist Graph Theory

Video thumbnail

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

Video thumbnail

Bipartite Graphs with Isolated Vertices | Graph Theory, Complete Bipartite Graphs

We know what a bipartite graph is, and we know about complete bipartite graphs. But how do these definitions work with isolated vertices that have no neighbors? We'll go over just that in today's graph theory lesson! Remember that a bipartite graph is a graph whose vertices that can be pa

From playlist Graph Theory

Video thumbnail

What are Complete Bipartite Graphs? | Graph Theory, Bipartite Graphs

What are complete bipartite graphs? We'll define complete bipartite graphs and show some examples and non-examples in today's video graph theory lesson! Remember a graph G = (V, E) is bipartite if the vertex set V can be partitioned into two sets V1 and V2 (called partite sets) such that

From playlist Graph Theory

Video thumbnail

OCR MEI MwA D: Graph Theory: 07 Bipartite Graphs

https://www.buymeacoffee.com/TLMaths Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dea

From playlist OCR MEI MwA D: Graph Theory

Video thumbnail

Multigraphs - Graph Theory

Introduction and overview of multigraphs in graph theory

From playlist Graph Theory

Video thumbnail

Every Tree is a Bipartite Graph

This video explains how to show that a tree is a bipartite graph. mathispower4u.com

From playlist Graph Theory (Discrete Math)

Video thumbnail

Bipartite Graphs: Determine a Matching of A if Possible

This video explains how to determine a matching of A in a bipartite and how to use Hall's Marriage theorem to explain why there I not a matching of A in a graph. mathispower4u.com

From playlist Graph Theory (Discrete Math)

Video thumbnail

Graph Theory: 09. Graph Isomorphisms

In this video I provide the definition of what it means for two graphs to be isomorphic. I illustrate this with two isomorphic graphs by giving an isomorphism between them, and conclude by discussing what it means for a mapping to be a bijection. An introduction to Graph Theory by Dr. Sar

From playlist Graph Theory part-2

Video thumbnail

Irina Gelbukh 2023: The Reeb graph of a smooth function encodes the function class and manifold type

Title: How the Reeb graph of a smooth function encodes the class of the function and the type of the manifold Abstract: The Reeb graph of a function is a space obtained by contracting connected components of the function's level sets to points. Computer scientists mostly deal with Morse f

From playlist Vietoris-Rips Seminar

Video thumbnail

Graphs In Data Structures | Graph Representation In Data Structure | Data Structures | Simplilearn

This data structures tutorial is dedicated to helping beginners understand the graphs in data structures. In this tutorial, you will understand the fundamentals and terminologies of the graph data structure, their types and their representation using different methods. The graphs in this t

From playlist Data Structures & Algorithms [2022 Updated]

Video thumbnail

What are Planar Graphs? | Graph Theory

What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t

From playlist Graph Theory

Video thumbnail

Lecture 19 - Degree Sequences & Invariants

This is Lecture 19 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2019.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

Empty Graph, Trivial Graph, and the Null Graph | Graph Theory

Whenever we talk about something that is defined by sets, it is important to consider the empty set and how it fits into the definition. In graph theory, empty sets in the definition of a particular graph can bring on three types/categories of graphs. The empty graphs, the trivial graph, a

From playlist Graph Theory

Video thumbnail

What is the limit of a sequence of graphs?? | Benjamini-Schramm Convergence

This is an introduction to the mathematical concept of Benjamini-Schramm convergence, which is a type of graph limit theory which works well for sparse graphs. We hope that most of it is understandable by a wide audience with some mathematical background (including some prior exposure to g

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Vertex Cuts in Graphs (and a bit on Connectivity) | Graph Theory, Vertex-Connectivity

What is a vertex cut of a graph? And how can we use vertex cuts to describe how connected a graph is? We have discussed cut vertices and connected graphs before, but by tying them together in a way, we are able to characterize different levels of connectivity in graphs. The focus of this l

From playlist Graph Theory

Video thumbnail

Vertex Connectivity of a Graph | Connectivity, K-connected Graphs, Graph Theory

What is vertex connectivity in graph theory? We'll be going over the definition of connectivity and some examples and related concepts in today's video graph theory lesson! The vertex connectivity of a graph is the minimum number of vertices you can delete to disconnect the graph or make

From playlist Graph Theory

Video thumbnail

Lecture 10 - Data Structures for Graphs

This is Lecture 10 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2007. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/2007/lecture10.pdf More informa

From playlist CSE373 - Analysis of Algorithms - 2007 SBU

Video thumbnail

Lecture 20 - Trees and Connectivity

This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

Graph Neural Networks, Session 2: Graph Definition

Types of Graphs Common data structures for storing graphs

From playlist Graph Neural Networks (Hands-on)

Related pages

Flow network | Graph theory | K-vertex-connected graph | Graph (discrete mathematics) | Vertex (graph theory) | Complete graph | Directed graph | Biconnected component