Intro to Directed Graphs | Digraph Theory
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- čas přidán 2. 06. 2024
- What are directed graphs, or digraphs as they are often called? We introduce digraphs and some related terms in today's graph theory lesson!
A directed graph is like a simple graph, except the edges of a digraph have - you guessed it - direction! Thus, we will see we need to use ordered pairs to describe edges of digraphs. For example, an edge going FROM the vertex u TO the vertex v is represented by the ordered pair (u, v). We say u is adjacent to v, and v is adjacent from u.
The number of edges coming out of a vertex (equivalently - the number of vertices a vertex is adjacent to) is the outdegree of the vertex. The number of edges going into a vertex (equivalently - the number of vertices a vertex is adjacent from) is the indegree of the vertex.
We call the directed edges of a digraph "arcs'. Thus, there can be two distinct arcs (u, v) and (v, u) that have the same end-vertices. Such edges are called parallel edges and DO in fact form a cycle of length 2.
How does the first theorem of graph theory work with digraphs? Think about that! Here is my lesson on the first theorem if you don't remember it: • The First Theorem of G...
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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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: vallow.bandcamp.com/
Vallow Spotify: open.spotify.com/artist/0fRtu...
Vallow SoundCloud: / benwatts-3
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lol thanks for the editing. other viewers really appreciate that too i'm sure. personally i try to follow every single word and definition you speak etc etc, and i can't ask you in real time, in case i am confused, so in my opinion this shows a tremendous amount of responsibility on your part. and dedication to the viewers
Thank you for the comment Luciano! No doubt I'd have many more videos, and many more errors, if I were looser in my production process. There are many lessons I've scrapped due to a single misspoken sentence which I deem not easily fixable. My general philosophy is to trash a video with an error unless that error can be corrected with a very minor edit such as cutting it out completely [which is impossible if the error was present in an important point], or a very brief caption, or occasionally a re-shoot is possible for a specific section without making the edit too jarring. There are some videos I made at this whiteboard where I said something wrong, but I said it while my back was turned, so I re-recorded the voice over for that section. In other situations where I say something wrong without my back turned, I think having the voice over not match my mouth is too jarring, so the video gets trashed. Inevitably, errors slip through anyways!
@@WrathofMath you're an extremely thoughtful man. keep that up, dude! it's made you considerate to your viewers
Fantastic lesson. Very helpful for those of us who learn better with examples. Really appreciated!
Thanks a lot Chris! I am glad it helped and be sure to let me know if you ever have any video requests!
Hi Wrath of Math, your videos are life-saving but I request you please organise them in a playlist that helps to cover those that are inter-related and we are missing.
Thanks for watching and I am glad you have found them helpful! Are you aware of my Graph theory playlist? czcams.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Or are you asking for some other sort of playlist? I have plenty more graph theory lessons I plan on creating for the graph theory playlist, more than 200.
@@WrathofMath thanks for giving the link. This helps me a lot. Your lectures are life savers.
Love and support from INDIA .
I love your videos and really appreciate the great work you are doing for math enthusiasts out there :)
Thank you!
That's helpin a lot man, we appreciate.
Glad to help! Thanks for watching!
Great video! It would also be helpful if at the end of the video you step to the side for a bit so people can take screen shots of the board
Thanks, Paul! I try to make that not necessary, by getting out of the way of the board fairly often throughout the lesson, I'll try to be more aware of that going forward to make sure you can get a good shot of it if needed!
Very well explained! Thank you
Glad it was helpful!
Amazing video. No wasted time, and straight to the point. Helped my with my Discrete Math course.
Thanks a lot! I'm glad it helped and be sure to check out my graph theory playlist if you're ever looking for more lessons! czcams.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Please make a video on graph enumeration and cutwidth in a directed graph.
Thank you so much!!! I can finally answer my homework
You're very welcome, I'm glad it helped and thanks for watching!
may i favor? sorry i don't know how to this
Given the sets A and B and the R such that a R b iff b divides a
Let A= { 1, 2, 3, 4, 5, 6, 9,12 }=B
-Digraphs
Is it possible to form a digraph between 2 sets??
this is so much better than my own professor explaining things. thank you! it makes sense now
Glad to hear it, thanks for watching and let me know if you have any questions!
thanks for the video....it is very clear
My pleasure, glad it was clear and thanks for watching!
can you cover directed acyclic graphs and topological order my exam is in 10 days. Really appreciate your videos!
Learning more from you than from school
I'm glad to be able to help!
you are a legend
agreed. helped to understand digraphs a bunch :D
Glad to hear it! Thanks for watching! :)
niceeeee video!!! thx so much! ❤
My pleasure, thanks for watching! If you're looking for more graph theory, check out my playlist! czcams.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Well explained...cool !😎
Thank you!
Sir. ....I need some basic questions based on the digraphs.....
Thanks for watching and I have more directed graphs lessons on the way - is there a particular topic you'd like to see covered soon?
@@WrathofMath sir I need major parts that is used to explain about the digraphs
Cool thanks!
Thanks for watching! Let me know if you ever have video requests!
Oh man, this stuff is so hard I want to di.
/jk, but thanks for helping us through it!
thanks a lot..
No problem, thanks a lot for watching!
Epic❤
Thank you!
thx a lot
My pleasure, thanks for watching!
he looks like andy bernard
Thanks for watching! I don't know anything about Andy Bernard so I can't make any clever joke, but I looked him up and I don't really see it. Alas, Bernard is in the eye of the beholder!
Bump if you came to watch this from MCIT 592
I like how you speak
Thank you - I try to speak very clearly!