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The beautiful math behind six degrees of separation.The simulations are now added below!To play around with the simulations in the video, you can follow these links: Disease spreading - https://www.veritasium.com/simulation2

Preferential attachment - https://ve42.co/barabasiAlbertSim

Comments

James Zaki

Brilliant! Absolutely loved this <3

TTST

<3 indeed. Looking forward to the network simulation code --- github?

Patrick W. Gilmore

Amazing information. I had no idea you needed so few "shortcuts" to transform a fully clustered network into close to the same degrees of separate as a fully random network. It is really surprising. Which leads me to my question: I get the results of the math, but you did not dive very deeply into WHY it works that way. Maybe a sequel video? Or should we get Grant or Brady to do it? :)

veritasium

Apologies, I should have added it to the description here too. It's now been added! - Matt, Publishing Lead

James Zaki

And coincidentally we had dinner with a friend once in Australia... Where do tenuous "shortcuts" fit in the model :p

Michael Hobbs

The animation that showed how, as a network grows, hubs form automatically - It quickly looked very much like a map of Eastern Massachusetts. There was no planning of settlements or roads in those days. Boston itself quickly became a hub, but then villages outside of Boston also became smaller hubs. See the Newtons for a grea example.

Michael Hobbs

Hubs also exist in the human 6 degrees situation. I worked at Microsoft in the '90s, so I'm only a two degrees away from Bill Gates. But he's connected to a huge number of people all around the world. Because I have a closer-than-average connection to a major hub, I might be only 5 degrees away from a huge part of humanity.

veritasium

Great question! And I think the key reason behind what you're getting at is that one shortcut doesn't just drastically reduce one path length - it drastically reduces many path lengths. And the bigger the network, the more paths are affected by a single shortcut AND the greater the reduction on each individual path. - James, writer for this video.

Stef Kuypers

I watched the video twice now. It's so fascinating! I started wondering something. Could it be that in today's world we get clusters around ideology? Could it be that clusters around a certain ideology have less shortcuts with nodes from other ideologies? If that would be the case,cCould it explain, at least in part, the state of the world today?

Robert Blackwell

Terrific video. Have you ever thought about using this to identify customer clusters?