Introduction to Graph Theory: A Computer Science Perspective

[@OliFarhaan]

I was unable to take admission to an engineering college to pursue Software Engineering due to my financial conditions. But I never lost hope I am studying on my own self and I feel privileged that I came to know about your channel. Thank you so much for such valuable content.

[@realdealholyfield9616]

Are you indian or paki?

[@harrykekgmail]

I wish you success

[@OliFarhaan]

@@harrykekgmail I wish you too :)

[@HghgBoovier]

I am a self-taught software developer with an established career. you can do this too. university is not required. the best advice to all readers is to start with web dev because it is the easiest path to starting a career. then on your own time study CS and interesting problems - because of this you will gain a fabulous education and your career will advance. good luck Ali Farhan

[@chafikthewarrior]

I am an autodidact Data Scientist, i started with Web development and i did everything using only google, no school. You can do it but you need to be 10 times better than the others may god help you in your journey.

[@einsteinnewton7121]

3Blue1Brown of Computer Science. Brilliant video.

[@vijaykumarreddyalavala3713]

Absolutely.

[@IsaacJoshi]

When I was watching this I thought hmm why does 3B1B's voice sound different

[@genericusername1243]

haha even i thought so

[@gauravarya8952]

Absolutely Brother. Such nice content in this vast ocean of copy cat junks.

[@kenhaley4]

@@KonigKlack They are. He gives credit in the notes below the video.

[@zamoqi]

4 years into software engineering and had to refresh the knowdlegd on this. SO far the best explanation of such complex and abstract for many topic graphs. A true GEM video. Thanks!

[@blackshadowproductions5144]

I'm studying by myself and I can tell this video has helped me a lot, not only due to the perfect explanation but also because of the downright great representations of what was being said. Thank you a lot, your work has been helping a lot of people!

[@gauravnikam8843]

Introduction :- 0:00 Why Study Graph :- 1:33 Definition :- 4:35 Terminologies :- 5:22 Types of Graph :- 8:32 Representation :- 10:15 Graph Problems :- 12:44

[@watchableraven3517]

Pro-tip: if you put the timestamps on the left, they'll line up better.

[@AlessandroBottoni]

This is by far the best video regarding graph theory I have seen in my (quite long) life. Extremely clear, extremely accurate and extremely useful. As "Einstein Newton" here said 8 months ago, this can be considered the 3Blue1Brown of Computer Science. Congratulations!

[@truffleshuffle314]

I was about to say that!

[@alonebuthappy33]

This is going to be one of the most popular study channel in the future ♥️

[@kingdel0xe]

There is a small mistake at 4:15 You would need to connect every point on a column with every other point on the same column same for the rows. Otherwise a graph coloring algorithm wouldn't work here, since graph coloring algorithms only test for the constraint that each neightbor has a different color.

[@thobiaslarsen8336]

Never seen a solution to a sodoku with graph theory! I just learned this to prepare for some competetive programming, I knew it was possible to solve using some disgusting nested for loops, but never knew graph would be a solution. Thank you!

[@youssefel-mahdy922]

I think it is the best video on KZbin that discuss and give an existing introduction about graph theory. It was my duty to thank you for this video!

[@FunMining]

This is a great channel, definitely will get much more recognitions in the future!

[@vladchira521]

I'm from the future! You were right. Just discovered this channel and I love it.

[@rushianokun]

It's happening

[@omaryahia]

I agree :)

[@PhysicsMosses]

I am from far future

[@gytzero]

Just found this, from the farer future

[@MythicalMaestro69]

Imagine Every Single Teacher in The World Teach Like HIM!! I mean there is no Teacher in my College who teach like him. His Explanations are clear and the way he presents his presentation is easy to understand and not boring to watch.

[@m322_yt]

well, I presume no teacher has a couple of weeks/months time to prepare a single lecture that introduces basic concepts

[@antontsvil245]

Im just can't thank you enough, this video was so enlightening that actually gives me a hope, it proves that I am able to learn and understand hard concept w/o expensive education. Eventually I would become a programmer. Thank you from the bottom of my heart

[@kaltenmacher]

An application of Graph theory in field of Pharmaceutical sciences is "Network Pharmacology". A software named Cytoscape is used to construct networks displaying connections between drugs, targets and diseases. This video reminded me of this and now this whole concept has become more interesting.

[@sliddjur]

As a network engineer, this is really interesting! I visualize my networks with python and networkx and dot-graphs. Really fun!

[@aakdani11]

Dude the way of explained this topic is so amazing and you made it look so easy to understand, It is so hard to understand this topic from books for someone like me. Thanks alot for your help. GOD bless!!

[@MrKyltpzyxm]

I like the little bit at the end regarding the path through each vertex only once. Welcome to graph theory 101. After some foundational examples let's jump straight to proving that P=NP. lol

[@IshraqTanvir]

u are just the goat of cs explanation! the soothing bg music has made the video just wow! important is that investing just 16 minutes and learnt it all - about graphs is more than enough.......thank u very much Mr.x (as I don't ur name)

[@machinimaaquinix3178]

The amount of time and care taken to produce this video shows. This is my first time on this channel and i'm looking forward to going through it more.

[@L1Q]

thank you SO MUCH for always providing representation of everything in terms of data structures. this is a differences between a topic being complete jargon and an actually making practical sense

[@symonzhu9153]

wow never would've thought about sudoku like this - that's awesome!

[@KoraxLP]

Your videos are absolutely amazing ! Especially your recursion video helped me immensely. Looking forward to more of your work. Keep going, this channel is going to be big! The video quality is just soo goood.

[@Reducible]

Thank you! Glad you find these videos helpful and yup I have so many ideas for content so don't plan on stopping any time soon :)

[@adriantee5219]

Beautifully explained and easily understandable to someone who knows little to nothing about graph theory or computer science. Keep up the good work!

[@NaveenKumar-os8dv]

If everyone was like you, study wouldn't not be tough. Thank you for this video and graph theory explanation. What you made is not just knowledge, but enlightment for me. You do it like its a cake to you, and I actually understand your explanation.

[@Thegamer-kf8zz]

I love the mission of this channel! We need more interesting ways to delve into computer science for people who don’t want to sit down for 2 hours to understand fundamental (often complex) computer science topics!!! KEEP UP THE GOOD WORK!

[@nosult3220]

Taking this as a grad level course rn. Its very stimulating for visual learners

[@MangoLassiYT]

this video was better than most videos on youtube related to graphs

[@partimecat]

Thank you for this video, I’ve been having a hard time motivating myself to start studying the graph theory chapter for my discrete math class, and this has helped me to finally open my textbook!

[@LowLevelLemmy]

Just discovered your channel. I'm about to binge everything you've made.

[@MCLooyverse]

I spent a few hours building a Graph data type in Haskell (and I do not remember why), and how I did it was as a (cyclic) list of pairs, where the first entry is the node value, and the second is a list of offsets of the node's neighbors. For example, it would represent the graph at 12:38 as [(0, [1,2,3]), (1, [4, 2]), (2, [3, 1]), (3, [2, 3, 4, 1]), (4, [4])]

[@rmt3589]

This is amazing! Reminded me of Vector Art, Wave Function Collapse, and Neuronets a lot. I have learned a lot, and deffinately want to learn way more!

[@robertcormia7970]

This was GREAT! I'm boning up on graph theory for cheminformatics, and this is providing a great foundation!

[@ahmedtawfiq3625]

Your videos are so well explained. Wish i had a teacher like you from high school...

[@hasanrants]

hats off, the production quality is mind boggling.

[@shreyageek]

What a clean video anyone can understand from images itself Thanks a lot for this

[@User-ty2ml]

i wish anyone who has interest in Graph, Watch this, the very first Day. Great Work, Thanks!!!!

[@trumanh1453]

Explain theories with clear diagrams and clear pronunciation. Great !

[@aramwis]

I'm so happy I got here. I'm a completely new to all of this yet I cam out understanding every single thing you just said. That was amazing. Thsnk you so much

[@boshay7832]

Thank you, I don't think I really understood adjacency lists until I watched this video.

[@goober3666]

this video is oddly beautiful, i absolutely despised this whole semester of discrete math but you kinda got me invested

[@hiryu87]

Superb breakdown of the subject. Had no idea before the video and now I really understand if fundamentally.

[@ankitshaw6307]

Amazing Explanation !! You explained such a complex topic in so easy to understand language. I learnt a lot today and also found out interesting ways to visualize a graph. Thank you !!!

[@yourlinuxguy]

Your video made me love the graphs. Thank you. Now I will look more into graphs, My friends find it difficulty but let me try it then we will find out.

[@bish-jyag3371]

Very nicely presented, clear and concise. You are the great teacher.

[@rangbuzz]

Brilliantly explained the concept of graph theory. Thank you.

[@ahmedtawfiq3625]

I will sit and watch all your videos one by one

[@haleynaga5671]

i cant read my college material for this particualr topic and found your videos, ist really great!!

[@wittyhumour29]

Great Introduction to Graph Theory. Amazing Explanation.

[@reubenvandermerwe480]

Great video. Simple and easy to understand, and yet it gives a great overview of graph theory concepts.

[@milajoy945]

Man!... your animations blow my mind 🤯 brilliantissime!!! Please keep doing them. I spent a moment on YT to find something understandable about graphs... and I found you! Thank you very much 🙏🏻🙏🏻

[@Victor_Marius]

I can not believe that I found and used the adjacency list by myself some time ago in a sketch without knowing it is a thing. I think it is the proof that the adjacency list is the most usefull representation

[@gunslingerstein]

the music was a very good touch to this video

[@daniahmed]

This was your first video that i saw amd let me say I'll always come here whenever there'll be a new math concept in CS that i want to understand. Cheers👍

[@cole1714]

Currently in an Algorithms and Data Structures class at my college. Man i love graphs

[@ducdao7275]

What an amazing video. I am about to take graph theory next semester, your video absolutely makes my hope high for that course now. Keep the good work, hope the channel to get more attention in the future. P.s: Is that possible if you can give a link to the script of the video or the summarize of what you talk about in the video. It will become a super helpful study material.

[@Reducible]

Thanks for the wonderful comment, I really appreciate it! That's an interesting idea, l think the easiest solution would be adding text files for scripts into the linked Github under a new folder. I'll try to remember to do that when the next video comes out (should be in 1 - 2 weeks). I will warn you, however, the scripts have a ton of notes on them about random animation files and things I need to remember when editing it all together that I probably won't have time to go back through and remove, so by no means will it be the cleanest "video script." Hope that's alright haha.

[@guysolo6542]

very good video, thank you so much, keep up the good work, watching 2 days before an exam

[@SebastianLopez-nh1rr]

I came here because of 3B1B, please keep up the good work. You've got great potential.

[@TampaCEO]

As a software engineer with nearly 30 years of experience, I believe that this is a subject that should be taught to ALL software engineers - especially those of us in information systems. As we migrate to a distributed solution of "micro services", graph theory is the perfect tool for effectively mapping the relationships between various applications, services, and data sources. Thanks for the introduction. I am moving forward with my training.

[@avenumadhav3568]

No of edges is same as number of neighbors has helped me to understand related topics in terms of visualizing, thanks!

[@sherlock_221]

The sudoku Example was the best! Please make more videos on graph theory

[@darthdias]

The video is very, very good! Thanks for all the work that went into making it. As a side note, I'd suggest you drop the background music as it makes harder to focus on the explanations.

[@fatimameryam6215]

Brilliant elegant explanation, wow. Thank you one thousand times !

[@sebbes333]

10:35 This matrix can be reduced to about half the size, since it is mirrored along the [(0,0), (4,4)] line, so either side of that line can be removed. (Depending on what's being graphed, you might want to either keep or remove the entries along that diagonal line).

[@alfredtomey]

Is there any programming language that lets you declare a “half-array”? If not, although you’re right, your RAM will be wasted anyway.

[@bluesillybeard]

@@alfredtomey in most Object-Oriented languages and any language that supports direct memory access, you can have an array of pointers, each pointer going to an array with its own length. Even if the language doesn't support direct memory access or objects, if it supports arrays one could emulate direct memory access. so, the answer is that every programming language that supports any kind of list whatsoever is capable of such an array.

[@raunakmitra7868]

The Sudoku example is outstanding and useful.

[@NottoriousGG]

You need content. Binge watchable sets of 20+ min videos on related topics from video to video. Trust the community. Keep it up great job.

[@SivatejaMattaparthi]

Thank you , definitely gave me some understanding in short time

[@Kyle-xk2rb]

As a CS student this is really good content. Love all the videos you make!

[@sooniesleardamer3871]

Keep on going! Your channel is just amazing! (Watching from France)

[@shashankkaryakarte8463]

best video for introduction to graphs....

[@markomozina7894]

Another great one. Can’ t wait for more:)

[@zaidmermam2524]

absolutely amazing explanation!

[@azatecas]

Why didnt i find this channel sooner? Love this

[@saipan1970]

Fantastic, just needed info for programming.Thank you.

[@patrickmayer9218]

*Graph theory is naturally applicable to things like social networks (i.e. recommending users friends of their friends). *Degree of Node - # of connections (edges) that node has. *Cycle - Path between nodes that starts and ends on the same node. *Directed Graphs - Type of graph where edges only go in one direction (you can't "retrace your steps"). *Weighted Graphs - Type of graph where edges have different values rather than just 1.

[@AssemblyWizard]

2:53 Ironically I thought Sudoku would be the first example lmao, but well played

[@andy-kg5fb]

I love this style of video.

[@williammasferrer9067]

Great video !!! It Accomplish his goal of giving an introduction on the topic.

[@ryanmckenna2047]

Very nicely introduced, I hope you have some very complex cutting edge applications of graph theory to show off :)

[@xxmiamygirlxx]

very nice, thanks for the vizualisation and soothing music

[@mdegaris1972]

Beautifully explained. Thank you!

[@LoayAl-Said-j8p]

I love the experience or watching the video!, So immersive. and the content is kinda wholistic, Thank you so much!

[@pafloxyq]

It feels so great that Grant has inspired people to follow this cool way of explaining things, keep up !!!

[@navneet5084]

Please make more content on Graphs!!

[@mikeofallon]

Excellent intro to graphs. I'd like to find applications for large dynamic graphs to solve complex problems.

[@renecabuhan1675]

Last week we have an assignment about airport routes, i solve it finally , but I didnt know the solution I use to solve it is called ajacentcy matrix. Thanks bro.

[@nachosncheez2492]

nice channel i just found it today, i like the concise summary's of topics

[@bikramm5553]

Wow!! Amazing Video. One the best video, I have ever seen.

[@mtd3v]

Just found you channel through this video. Great presentation.

[@thelegalsystem]

Algorhyme - by Radia Perlman " I think that I shall never see A graph more lovely than a tree. A tree whose crucial property Is loop-free connectivity. A tree that must be sure to span So packets can reach every LAN. First, the root must be selected. By ID, it is elected. Least-cost paths from root are traced. In the tree, these paths are placed. A mesh is made by folks like me, Then bridges find a spanning tree."

[@maxpalm7862]

Thank you very much, that was a great introduction. Much appreciated

[@shubhkhandelwal4822]

Thank you for existing!

[@rhinelandnagel7288]

This made my discreet mathematics fun

[@astroceleste292]

Thank you for putting subtitles

[@orionknight-o4l]

It was really helpful for my 7th sem

[@vijaykumarreddyalavala3713]

I can not believe all of this is for free

[@Artaxerxes.]

"What a time to be alive" as quoted by TwoMinutePapers

[@channagirijagadish1201]

Excellent Channel and very informative with rigor.

[@EW-mb1ih]

At 5:06, a small mistake: you should have writeen V = {0, 1, 2, 3, 4} and not V = {0, 1, 2, 3, 4, 5}

[@Syph_Silver]

thank you very much for this explanation !

[@MayankY2K]

OMG!! Great explanation, Great Presentation. Of course, going to crack university examinations with excellent points.😍😍 I'm confused about whether should I tell about this channel to my competitors or leave them on their fate.

[@carl-johanhorberg1399]

Brilliant. Impossible not to understand