Graph Theory - An Introduction!

[liyang8968]

awesome

[danielriodejaneirobr]

Thanks from Brazil!

[ilyn2208]

very helpful... thanks a lot.. you are a sharpie guy..!!!!LOL;)

[AleifrLeifrson]

Observation: the adjacency matrix is symmetric. =)

[TheCoolman5500]

fantastic

thank you very much

[patrickJMT]

@TheCoolman5500 u r very welcome : )

[sanwariaamir]

You are a savior. Thanks a ton..!!

[MsLillieG]

Thanks for the intro. Please post more videos on Graph Theory! I'm enrolled to take this class next quarter and would def appreciate the extra help.

P.S. You got me through Calc I-IV at my school :D

[GodlessPhilosopher]

Post the open questions!

[frederikcreemers]

thx for the lecture.

You said you didn't have many applications for adjacency lists.

They are very useful for storing a graph in a datastructure, if you don't have too many connections. If there are more connections, an adjacency matrix will be easier to search through. Also, in an undirected graph, you'll have a lot of redundant data in an djacency matrix.

[gv2416]

i really appreciate this video not being tedious to sit through :)

[gv2416]

thanks!

[CaffroX]

Thanks a lot, this video may very well make me pass my upcoming exam!

[praskuma]

Great explanation....

[alexwhb122]

thank you very much for this video! you are an amazing teacher. if you have time please make more graph Theory videos. i find it quite interesting.

[EliTeXHeRo]

@Oxydox Adjacency matrices are symmetrical providing the all arcs are two-directional - so an exception to the rule is found in a digraph where there are two arcs connecting a pair of nodes, with different directions, and different weights (providing the graph is a network).

[solde99]

Thank you man. I read about it several hours and after your explanation i finally understand it.

[TheSatanikOrder666]

this is very fascinating, what applications could I use this for in real life?

[fuzzyzero]

Nice work! I would like very much to see the open-problems list and especially if you have in mind something about digraphs and control applications :) Thanks & keep going

[jasmine27c]

thank youuuu! :D

[Muradss]

Dude you are a legend amongst teachers, NAY, a legend amongst men! You are clear concise and your explanations are beautiful. Thank you

[uiqbal10]

very well explained, thanks a lot lad

[needsmorsleep]

In my group theory course our definition of isomorphic is a metric preserving mapping...

[Xx420xZzSniperShotxX]

could v1 be connected to v5? or does it not go thru v4

[lhablyrose14]

THE BEST :">



[LIGHTSAT1]

you are an excellent teacher...

[coolmisskitkat]

Patrick can you cover concepts from modern (abstract) algebra?! Im a math major partly because of you! And upper division math is just not as great without you! Also, How did you learn all these concepts so well? I'm struggling in my modern algebra class, my first upper division, and I need your help. Thanks in advance!

[CAATMAN1]

Hi, i like your teaching method.  Sure would be nice if you continued to teach more graph theory

[wbbunga]

First of all thanks for this tutorial cause helped me a lot. Second of all i need your help in something. Soon i have exams about discrete Mathematics specifically logic, set and graph theory. Can you pls help me.

Reggards

Wil.

[drummer4371]

I have come to realise that my example if V1 is connected to itself (because of the loop), and connected to V2 and V3.

Then in an adjacency matrix, we can represent as

V1: V1, V2, V3 therefore will be represented as a 1 1 1

V2: V1, V3 therefore can be represented as a 1 0 1

V3: V1, V2, therefore can be represented as a 1 1 0

which gives the matrix: 1 1 1

A = 1 0 1 1 1 0

Thanks for posting on adjacency lists as I was able to work out the matrix, thought i would share this info.

[drummer4371]

Hi,

Regarding your Adjacency list this can be used to calculate an adjacency matrix.

i.e if you have a non directional graph with 3 nodes/vertices (v1, V2 and V3), and 3 edges and say we wanted to make v1 loop back to itself.

We can represent the graph as a three sided triangle with a loop on v1.

Because it is a graph with 3 vertices, then it will be represented as a 3X3 matrix.

From your example on Adjacency lists....

[duktape1976]

Hi Patrick. Thank you very much for your generosity. You have a knack for explaining complex subjects simply. I look forward to more tutorials!

[patrickJMT]

@Oxydox yes, i made a mistake and put the 1 in the incorrect spot. there are now text annotations pointing it out.

[QuantumMaths]

YES!!!!

[sesposito7]

Please keep these coming, Patrick.. I just began self studying graph theory and I'm finding it extremely interesting. Glad to see you working with graphs, also.

I'm currently using a decent text, but I was wondering if you could recommend one so that I may supplement the one I'm using..

[sjsawyer]

Awesome Patrick! I actually just began to look into graph theory last week. I'll be taking my first course on it in January so I'm sure any vids you post relating to it will be extremely helpful :)

[aznlalaland]

Why are you so smart????

[patrickJMT]

@aznlalaland ha, i really am not. people on youtube give me too much credit. i spent a ton of time in college studying a lot of math. some of it actually started to make some sense : )

[aznlalaland]

@patrickJMT Math major here. Right now, I am studying ideals and Q(D) fields. The concepts are easy but proving props is the hard part. This is why I say you are smart. Not everyone fully grasps all definitions and remember every single prop. Oh, I have a question. Should I take combinatorics or Galois theory? Which one is harder and which one will benefit me in the long run? And what was your focus in grad school? Love you still.

[eegiievol]

@aznlalaland cuz he is left handed

[patrickJMT]

@filmcruiser88 i am 100% for sure that graph theory gets used a lot in logistics

[flopski]

It's used in electronic engineering too.

[yyourfacee]

o god as soon as he drew the graph, it reminded me of directed acyclic graph from computer science T.T

[Tsukasa171]

you made a little error on the matrix, you put 1 for v4 and v5, but v5 is connected to v4 and v6, not v4 and v5. Very helpful!

[patrickJMT]

@Tsukasa171 doh, thanks! i will put in some text annotations!

[VSpectrum]

Thanks for this!! =D i'd love to see more of graph theory vids. once again thanks a mil for this

[zengrz]

man have been waiting forever! THX

[Vorbis5]

Sweeeeeet!

[sk8teh14]

I think this stuff was used to find Graham's number.

[sk8sheep24]

Hey, just thought I should point out, in your Adjacency Matrix you put a 1 in the V5-V5 place, instead of the V5-V6. I really like your videos, since you have a great talent for explaining things!

[Taowhr]

Oh my god, patrick! You are doing graph theory now??? YOU ARE GOD'S SENT!!!

[Skynt]

I love this! I'm competing in the Putnam Competition, and so these kind of videos are really useful.

[MrEinsteinz]

Awesome.