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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.

I am trying to aim for quality over quantity with these videos. If you want to support the channel consider checking out my patreon: patreon.com/NotDavid

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 hypernetworks 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 SmallWorld Functional Network in Cultured Neurons"
Julia H. Downes et. al.
and
"Selforganization 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.
The brain model is by Anderson Winkle, licensed under Creative Commons AttributionShareAlike 3.0 Unported License. The original work can be found at https://brainder.org/brainforblender
Notable tutorials used:
Making (Procedural) Membranes | Blender for Biochemists | Geometry Nodes by Brady Johnston
Special thanks to thebasemesh.com for providing some of the assets.

MUSIC (in order)

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Loafy Building x Hoffy Beats – Sleepless Wonder
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Cauffee – Vague Familiarity
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Purrple Cat – Cold Pizza
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Kevin McLeod/ Incompetech
https://incompetech.com

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Cauffee – Unreleased