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In this video I run with an off-hand comment I made last time about applying network theory to pokemon. Even if you don't like pokemon I hope you stick around - the point here is not to look at pokemon, but rather showcasing an example of applying rigerous real world mathematics to something a bit silly, with the hopes of reaching students who think math is boring.

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

Submitted as part of Summer of Math Exposition 2022

#maths #education

footnotes:

1. 0:54 Link to Jupyter notebook. Please note: a contributor has made an amazing expansion to the code that looks at the dual type network and which is included, and ... yeah... it's significantly more complex. For the sake of keeping the code organized/safe I will not be accepting new merges/commits but you are of course welcome to download it and edit your own local version and let me know in the comments if you discover something interesting https://github.com/notDavidsGit/pokem...
2. 1:13 Kpop fan club network: https://www.abacademies.org/articles/...
Starwars social network: http://evelinag.com/blog/2015/12-15-s...
3. 2:53 We could also treat any undirected network as a directed network where theres a link going both ways, but this is often conceptually combersome
4. 3:06 Self loops are often debated about whether or not they should be kept. For example, in a friendship network where nodes represent people, and links represent friendship between those people, should you be linked to yourself? Philosophically I guess yes, but does that actually add anything to the analysis in the end?
5. 3:15 I really do mean it when I say we are leaving out a lot. I didn’t even go into type resistances and immunities as I felt that would over-complicate the analysis and figures, without actually adding much to the actual “meat” of the theory. For those curious, the type advantage network is probably best described as a WEIGHTED directed network, whereas we considered only a BINARY directed network here.
6. 5:15 These angle brackets are the physics notation for the average of a quantity.
7. 5:28 Theres another property that I didn’t talk about here thats worth thinking about if your keen - the average directed degrees are equal to half the average un-directed degree.
8. 6:09 I should emphasize here that the criterion for connectedness is that ANY node can reach ANY other node. So while you can reach the normal type following directed paths, you cannot reach any other node from the normal type.
9. 6:28 In a lot of cases even if we know a network should be directed, we cant measure it for technological reasons. For example, in the brain, inferring which neurons are “downstream” from which other neurons is extremely difficult to measure for anything more than a handful of cells.
10. 7:19 This is primarily a list of functions from the networkX python library if you are interested in playing with them.
11. 8:55 The technical term for this is network reciprocity. Because no element is advantageous against an element it connects back to, the reciprocity is zero. Important note: reciprocity does not consider self-loops!


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Justin M.
Thank you to nintendo who hopefully is not going to sue me :(