Network Theory: The study of relationships

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Network theory is the study of relationships - whether it be connections between characters in your fravourite TV show, real people, computers, or anything. Here we take a guided tour of what networks are, how they arise in nature, and what they can teach us.

CITATIONS/ FOOTNOTES:

1. 3:15 Fragility of a network can be defined by the quantiative and qualitative changes in the network structure due to the removal of one or many nodes (or links). This can be done randomly or in a targeted fasion. A ring network is susceptible to both. Something like a small world network (defined later in the video) is susceptible to targeted removal of nodes but not random removal of nodes. This is an important consideration in critical infrastructure networks (power grids, internet, etc.).

2. 3:54 This is optimistic as I only considered unweighted undirected networks. For either directed or weighted networks, this number would expload even faster. Don't worry if this doesn't mean anything to you though.

3. 4:19 The two graphs on the left are called "random" networks (which will potentially be a future topic) where as the one on the right is potentially a small world network.

4. 4:44 In network neuroscience there is the distinction between structural networks (e.g., following the connections of physical neurons or brain regions) or functional networks (e.g., formed by looking at which neurons activate together). We will touch on this more in a future video on network inference.

5. 5:15 6 Degrees of Seperation and the Kevin Bacon number are really the same thing more or less. There are also a lot of problems with the original 6 Degrees of Seperation experiment, which we will touch on in the network inference video in the future.

6. 5:26 This is not a rigerous definition of small world networks. Typically one has to consider whats called the average path length, and how it scales as a function of the number of nodes. In many real world systems though this is difficult to do as you can't simply add nodes.

7. 5:42 For example, for the year of 2019, 15 airports accounted for 10% of world wide travel, despite the fact that they only acount for 0.03% of airports.

8. 6:16 Its a bit more complicated this as these are actually typically formed by what are called hyper-networks or hypergraphs where in we have different types of nodes. You wouldn't want a purely small world network because, as mentioned in citation 1, small world networks are susceptible to targeted network attacks.

9. 6:27 Paper: "Emergence of a Small-World Functional Network in Cultured Neurons"
Julia H. Downes et. al.
and
"Self-organization of in vitro neuronal assemblies drives to complex network topology"
Prciscila C. Antonello et. al.
(the second has a preprint on Biorxiv and should be free to access there)

10. 7:01 Much of this analysis has been attributed to Jacob Moreno, though it appears that the majority (if not all) of this work was conducted by his assistant Helen Hall Jennings as Moreno was not mathematically motivated nor was he particularly interested in systematic research. Unfortunently this is not uncommon in science.

Footnote 7:50 -- Bojack Horseman

11. 8:06 If you're interested in more, Networks: An Introduction by Mark Newman is a great introduction into the field.

12. This is from Evalina Gabasova's 2015 blog entry "The star wars social network" (you should be able to just google that), I highly recommend it. I unfortunently was not able to find the kpop group network again. If I find it in the future I'll edit this.

CREDITS:
Most assets created by myself.
Notable tutorials used:
- Making (Procedural) Membranes | Blender for Biochemists | Geometry Nodes by Brady Johnston

MUSIC (in order)

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- Loafy Building x Hoffy Beats – Sleepless Wonder
- Provided by Lofi Records

📥 | Download this music (free)

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- Cauffee – Vague Familiarity

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- Purrple Cat – Cold Pizza
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- Kevin McLeod/ Incompetech

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- Cauffee – Unreleased

[dialectphilosophy]

You have a great animation style and clarity of presentation! Keep up the good work - people will find your channel

[zaraz]

As a high schooler who is considering a major in math but afraid of how abstract it might get, this video is seriously tempting me to take the leap anyway. I really love the way you visualized the concept (by the way, what did you use/how did you animate your video? I'm obsessed with the style) and can imagine it being applied to so many different fields. Fascinating.

[erikhaag]

I love how many references to memes and games there are in these videos, like TIS-100 at 8:10 for example. It's nice to know that people know a lot of obscure games like that.

[daveys]

That last point is key. People seem to learn better if they can hook the new learning onto something that already makes sense to them. Using relevant examples also makes the stories stick better.

[ahmedmansourbourassine]

dude !! your channel is sooo underrated! great content, great animation and a good humour too ! keep up the awesome work and little by little you will become wayyy more known.

[Me-]

I just wanted to say that I love your videos. If you ever need any help with research or something (for example in your latest video, counting the space between ummm’s) Im down to help. I feel like this channel is awesome, and deserves way more, and a little help cant hurt.

[gonzacont]

Network theory phd student here, and new subscriber to your channel. I think there are many interesting ideas which you can animate, you already touched some great points in the pokemon video. And the animations are great, congratulations!

I would like to point out a misconception in this video, which may deserve a future video as I find it quite interesting. You make a relation between hubs & small world networks, but that is not necessarily true. In fact, the first model for small-world networks (by Watts and Strogatz) does not feature hubs, instead it focuses on the existence of bridges which appear by a rewiring procedure.

Networks with hubs are usually called scale-free, with the first model being that of Barabasi and Albert, and AFAIK they need not be small world. They are if hubs are connected to each other, if they are far apart they need not be. But yeah, in general they will be.

Anyway, great content, hope to see more in the future!

[abdallahatia]

Man I am so glad your recent video blew up and showed me this channel because I really really love it. Can’t wait to be here to watch it grow

[trukaiser]

Speaking of a small world, this reminds me of Structuralism. It's like Mathematics meets Sociology and, speaking purely "objectively", I find awesome!!

[Steaks]

I would've LOVED to see a 20 minute deep dive into the math of graph theory and how it relates to real world problems

[Alex-hongry]

Hi, sorry I’m new to your channel…but..this is some of the most amazing animation I’ve ever seen….the planning…the minuscule details….its mind blowing. Please, tell me how you got to this level, what resources or programs you use and how I might even begin to start to learn to do something like that. I have seen tutorials for many things but this just seems……beyond what one person could achieve? Casually??!! Any insight appreciated. I feel like I’ve just found a huge blind spot in my understanding!!!

[Zaniahiononzenbei]

Using TIS-100 in your animations is so cute. Love it.

[Eniac]

8:05 the game that is showing in the PC is TIS-100. It a fun game by zectronics

[robinsonbadell]

Recently found your channel, and may I say... I have enjoyed everything that has been mentioned, keep it up!

[Victual]

Awesome to see a math free view, but would also be super cool to see elaborated math versions :)

[gopherbarney]

I just gotta say thanks for making videos man. You're helpful.

[not_David]

Thanks to everyone for the amazing support in my previous video! In the next video we will actually look at how one would apply network theory and some of the metrics being used.

[uoitauz]

crazy good video! I just discovered you channel from you video about "uhmmm". keep up the good work, people like you spread curiosity and the desire to learn cool stuff like math!

[cashewABCD]

Good stuff Not David, glad to find another excellent channel. Wishing you the best.

[cognitivebiasalpha]

You are taking on subjects, which are of high interest to me. Your production quality is way above what add income could pay for.
How do you do that?
Asking for a friend...