In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.
There are two distinct notions of multiple edges:
Edges without own identity: The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes.
Edges with own identity: Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges.
A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two.
For some authors, the terms pseudograph and multigraph are synonymous. For others, a pseudograph is a multigraph with loops.
Undirected multigraph (edges without own identity)
Graph - Multigraph
Watch More Videos at:
https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Mr. Arnab Chakraborty, Tutorials Point India Private Limited.
published: 29 Jan 2018
what is a multigraph
published: 21 Mar 2018
what is a directed multigraph
published: 21 Mar 2018
Graph (4/7) Multigraph | Prof. Glenda R. Tandingan
#graph #multigraph #discretestructure
published: 14 Nov 2021
MULTI GRAPH || GRAPH THEORY & TREES || DISCRETE MATHEMATICS || OU EDUCATION
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1. Graphs, Finite & Infinite Graphs, Directed and undirected graphs, Simple, Multigraph, psuedograph
Radhe Radhe
This is first vedio of graph theory playlist. In this vedio, some notions like Graphs, endpoints, Finite & Infinite Graphs, Directed and undirected graphs, Simple graph, loops, Multigraph, psuedograph, simple directed graph and directed multigraphs are discussed with the help of examples.
I hope you will be benifitted by this vedio.
For coming vedios on graph theory, you can visit the following playlist:
https://www.youtube.com/playlist?list=PLq76ktDFTJEJneLcRDT4X01ZMRJpzDFx-
Wish you all the best !!
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Overview of Loops in Graph Theory | Graph Loop, Multigraphs, Pseudographs
What are loops in graph theory? Sometimes called self loops, a loop in a graph is an edge that connects a vertex to itself. These are not allowed in what are often called "simple graphs", which are the graphs we usually study when we begin studying graph theory.
In simple graphs, loop edges are not allowed. Also, multiple edges are not allowed to join the same pair of vertices in a simple graph. A pair of vertices is either joined by 0 edges or 1 edge.
Multigraph is a term used to refer to a graph where multiple edges are allowed, and loops may or may not be allowed. Pseudograph is a term usually used to refer to a graph where multiple edges and loops are allowed.
You might remember that with simple graphs, we defined an edge as being a 2-element subset of the vertex set. So an edge j...
published: 10 Jan 2019
Multigraphs - Graph Theory
Introduction and overview of multigraphs in graph theory
published: 27 Aug 2011
Graph (6/7) Multigraph | Prof. Glenda R. Tandingan
Graph - Multigraph
Watch More Videos at:
https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Mr. Arnab Chakraborty, Tutorials Point India Priva...
Graph - Multigraph
Watch More Videos at:
https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Mr. Arnab Chakraborty, Tutorials Point India Private Limited.
Graph - Multigraph
Watch More Videos at:
https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Mr. Arnab Chakraborty, Tutorials Point India Private Limited.
GATE Insights Version: CSE
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or
GATE Insights Version: CSE
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Planning to take coaching on https://unacademy.com/
here is a code for 10% off PLUS1BPK1
Link for our website and app where u can get the pdfs
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https://education4fun.com/
Ultra Fast and Temp access
http://bit.ly/lets_clear_it
Sem 8 Notes
https://bit.ly/cse-sem-8
Still Confused DM me on WhatsApp
(*Only WhatsApp messages* calls will not be lifted)
GATE Insights Version: CSE
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or
GATE Insights Version: CSE
https://www.youtube.com/channel/UCD0Gjdz157FQalNfUO8ZnNg?sub_confirmation=1
Planning to take coaching on https://unacademy.com/
here is a code for 10% off PLUS1BPK1
Link for our website and app where u can get the pdfs
https://play.google.com/store/apps/details?id=net.itsTimeforFunITF.education4fun
https://education4fun.com/
Ultra Fast and Temp access
http://bit.ly/lets_clear_it
Sem 8 Notes
https://bit.ly/cse-sem-8
Still Confused DM me on WhatsApp
(*Only WhatsApp messages* calls will not be lifted)
1. Graphs, Finite & Infinite Graphs, Directed and undirected graphs, Simple, Multigraph, psuedograph
Radhe Radhe
This is first vedio of graph theory playlist. ...
1. Graphs, Finite & Infinite Graphs, Directed and undirected graphs, Simple, Multigraph, psuedograph
Radhe Radhe
This is first vedio of graph theory playlist. In this vedio, some notions like Graphs, endpoints, Finite & Infinite Graphs, Directed and undirected graphs, Simple graph, loops, Multigraph, psuedograph, simple directed graph and directed multigraphs are discussed with the help of examples.
I hope you will be benifitted by this vedio.
For coming vedios on graph theory, you can visit the following playlist:
https://www.youtube.com/playlist?list=PLq76ktDFTJEJneLcRDT4X01ZMRJpzDFx-
Wish you all the best !!
Like, Share and Subscribe
Thanks
instagram.com/nishagodani
1. Graphs, Finite & Infinite Graphs, Directed and undirected graphs, Simple, Multigraph, psuedograph
Radhe Radhe
This is first vedio of graph theory playlist. In this vedio, some notions like Graphs, endpoints, Finite & Infinite Graphs, Directed and undirected graphs, Simple graph, loops, Multigraph, psuedograph, simple directed graph and directed multigraphs are discussed with the help of examples.
I hope you will be benifitted by this vedio.
For coming vedios on graph theory, you can visit the following playlist:
https://www.youtube.com/playlist?list=PLq76ktDFTJEJneLcRDT4X01ZMRJpzDFx-
Wish you all the best !!
Like, Share and Subscribe
Thanks
instagram.com/nishagodani
What are loops in graph theory? Sometimes called self loops, a loop in a graph is an edge that connects a vertex to itself. These are not allowed in what are of...
What are loops in graph theory? Sometimes called self loops, a loop in a graph is an edge that connects a vertex to itself. These are not allowed in what are often called "simple graphs", which are the graphs we usually study when we begin studying graph theory.
In simple graphs, loop edges are not allowed. Also, multiple edges are not allowed to join the same pair of vertices in a simple graph. A pair of vertices is either joined by 0 edges or 1 edge.
Multigraph is a term used to refer to a graph where multiple edges are allowed, and loops may or may not be allowed. Pseudograph is a term usually used to refer to a graph where multiple edges and loops are allowed.
You might remember that with simple graphs, we defined an edge as being a 2-element subset of the vertex set. So an edge joining vertex a and vertex b could be written as { a, b }. This could cause some confusion with loops because the set { a, a } is just the set { a }, because repeated elements are not recognized in sets. There are two solutions I have seen to deal with this problem.
The first solution is to simply embrace the problem, and define a loop as being a one-element subset of the vertex set. So if an edge in the edge set is a one-element set, you would know that refers to a loop.
The other solution is to use multisets, which are like sets, except for the distinction that multiplicity is considered in multisets. That is, the multiset { a } is not the same as the multiset { a, a }. The multiset { a } contains the vertex a with multiplicity 1 (1 copy of a), the multiset { a, a } contains the vertex a but with multiplicity 2 (2 copies of a). So a loop can also be defined as a multiset with one vertex of multiplicity 2, representing an edge that goes from one vertex right back to the same vertex.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
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What are loops in graph theory? Sometimes called self loops, a loop in a graph is an edge that connects a vertex to itself. These are not allowed in what are often called "simple graphs", which are the graphs we usually study when we begin studying graph theory.
In simple graphs, loop edges are not allowed. Also, multiple edges are not allowed to join the same pair of vertices in a simple graph. A pair of vertices is either joined by 0 edges or 1 edge.
Multigraph is a term used to refer to a graph where multiple edges are allowed, and loops may or may not be allowed. Pseudograph is a term usually used to refer to a graph where multiple edges and loops are allowed.
You might remember that with simple graphs, we defined an edge as being a 2-element subset of the vertex set. So an edge joining vertex a and vertex b could be written as { a, b }. This could cause some confusion with loops because the set { a, a } is just the set { a }, because repeated elements are not recognized in sets. There are two solutions I have seen to deal with this problem.
The first solution is to simply embrace the problem, and define a loop as being a one-element subset of the vertex set. So if an edge in the edge set is a one-element set, you would know that refers to a loop.
The other solution is to use multisets, which are like sets, except for the distinction that multiplicity is considered in multisets. That is, the multiset { a } is not the same as the multiset { a, a }. The multiset { a } contains the vertex a with multiplicity 1 (1 copy of a), the multiset { a, a } contains the vertex a but with multiplicity 2 (2 copies of a). So a loop can also be defined as a multiset with one vertex of multiplicity 2, representing an edge that goes from one vertex right back to the same vertex.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons
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Graph - Multigraph
Watch More Videos at:
https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Mr. Arnab Chakraborty, Tutorials Point India Private Limited.
GATE Insights Version: CSE
http://bit.ly/gate_insights
or
GATE Insights Version: CSE
https://www.youtube.com/channel/UCD0Gjdz157FQalNfUO8ZnNg?sub_confirmation=1
Planning to take coaching on https://unacademy.com/
here is a code for 10% off PLUS1BPK1
Link for our website and app where u can get the pdfs
https://play.google.com/store/apps/details?id=net.itsTimeforFunITF.education4fun
https://education4fun.com/
Ultra Fast and Temp access
http://bit.ly/lets_clear_it
Sem 8 Notes
https://bit.ly/cse-sem-8
Still Confused DM me on WhatsApp
(*Only WhatsApp messages* calls will not be lifted)
1. Graphs, Finite & Infinite Graphs, Directed and undirected graphs, Simple, Multigraph, psuedograph
Radhe Radhe
This is first vedio of graph theory playlist. In this vedio, some notions like Graphs, endpoints, Finite & Infinite Graphs, Directed and undirected graphs, Simple graph, loops, Multigraph, psuedograph, simple directed graph and directed multigraphs are discussed with the help of examples.
I hope you will be benifitted by this vedio.
For coming vedios on graph theory, you can visit the following playlist:
https://www.youtube.com/playlist?list=PLq76ktDFTJEJneLcRDT4X01ZMRJpzDFx-
Wish you all the best !!
Like, Share and Subscribe
Thanks
instagram.com/nishagodani
What are loops in graph theory? Sometimes called self loops, a loop in a graph is an edge that connects a vertex to itself. These are not allowed in what are often called "simple graphs", which are the graphs we usually study when we begin studying graph theory.
In simple graphs, loop edges are not allowed. Also, multiple edges are not allowed to join the same pair of vertices in a simple graph. A pair of vertices is either joined by 0 edges or 1 edge.
Multigraph is a term used to refer to a graph where multiple edges are allowed, and loops may or may not be allowed. Pseudograph is a term usually used to refer to a graph where multiple edges and loops are allowed.
You might remember that with simple graphs, we defined an edge as being a 2-element subset of the vertex set. So an edge joining vertex a and vertex b could be written as { a, b }. This could cause some confusion with loops because the set { a, a } is just the set { a }, because repeated elements are not recognized in sets. There are two solutions I have seen to deal with this problem.
The first solution is to simply embrace the problem, and define a loop as being a one-element subset of the vertex set. So if an edge in the edge set is a one-element set, you would know that refers to a loop.
The other solution is to use multisets, which are like sets, except for the distinction that multiplicity is considered in multisets. That is, the multiset { a } is not the same as the multiset { a, a }. The multiset { a } contains the vertex a with multiplicity 1 (1 copy of a), the multiset { a, a } contains the vertex a but with multiplicity 2 (2 copies of a). So a loop can also be defined as a multiset with one vertex of multiplicity 2, representing an edge that goes from one vertex right back to the same vertex.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: https://vallow.bandcamp.com/
Vallow Spotify: https://open.spotify.com/artist/0fRtulS8R2Sr0nkRLJJ6eW
Vallow SoundCloud: https://soundcloud.com/benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: https://www.patreon.com/wrathofmathlessons
Follow Wrath of Math on...
● Instagram: https://www.instagram.com/wrathofmathedu
● Facebook: https://www.facebook.com/WrathofMath
● Twitter: https://twitter.com/wrathofmathedu
My Music Channel: http://www.youtube.com/seanemusic
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.
There are two distinct notions of multiple edges:
Edges without own identity: The identity of an edge is defined solely by the two nodes it connects. In this case, the term "multiple edges" means that the same edge can occur several times between these two nodes.
Edges with own identity: Edges are primitive entities just like nodes. When multiple edges connect two nodes, these are different edges.
A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two.
For some authors, the terms pseudograph and multigraph are synonymous. For others, a pseudograph is a multigraph with loops.
Undirected multigraph (edges without own identity)