The beautiful math behind six degrees of separation. Sponsored by Incogni - use code veritasium at https://incogni.com/veritasium to get an exclusive 60% off.

If you’re looking for a molecular modelling kit, try Snatoms, a kit I invented where the atoms snap together magnetically - https://ve42.co/SnatomsV

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To play around with the simulations in the video, you can follow these links:

Disease spreading - https://ve42.co/wattsStrogatzSim

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

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A huge thank you to:

Duncan Watts, for creating the small-world model that inspired this video and expanding on his further work; Steve Strogatz, for telling the story with such clarity & humour; Albert-László Barabási, for revealing the the inevitability and impact of hubs; Mark Buchanan, for his insightful takeaways that pulled it all together.

Check out Duncan Watts’ books here - ve42.co/bookSixDegrees

Check out Mark Buchanan’s book here - ve42.co/bookNexusWorlds

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Chapters:

0:00 What is six degrees of separation?

4:23 Weak ties

11:05 How disease spreads

12:36 The paper goes viral

16:28 The long tail

24:03 A familiar dilemma

23:38 The Prisoner’s Dilemma

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References can be found here - https://ve42.co/networksRefs

Image and video references can be found here - https://ve42.co/networksVisuals

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Special thanks to our Patreon supporters:

Alex Porter, Alexander Tamas, Anton Ragin, Anupam Banerjee, Gnare, Ibby Hadeed, Jon Jamison, Juan Benet, Lee Redden, Meekay, Orlando Bassotto, Paul Peijzel, Richard Sundvall, Sam Lutfi, Ubiquity Ventures, Adam Foreman, Albert Wenger, armedtoe, Balkrishna Heroor, Bertrand Serlet, Blake Byers, Bruce, Dave Kircher, David Johnston, David Tseng, Evgeny Skvortsov, Garrett Mueller, gpoly, Jeromy Johnson, KeyWestr, Kyi, Marinus Kuivenhoven, Matthias Wrobel, meg noah, Michael Bush, Michael Krugman, Robert Oliveira, Tj Steyn & wolfee

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Writers: James Moore, Casper Mebius & Derek Muller

Producer & Director: James Moore

Editors: Peter Nelson & Jack Saxon

Camera Operators: Derek Muller & Casper Mebius

Animators: Andrew Neet, Emma Wright, Fabio Albertelli & Ivy Tello

Illustrators: Jakub Misiek

Assistant Editor: James Stuart

Researchers: Callum Cuttle, Aakash Singh Bagga & Gabe Strong

Simulations: Callum Cuttle, Gabe Strong & Ivy Tello

Sound Designers: Pavle Peric & James Stuart

Thumbnail Designers: Abdallah Rabah, Ren Hurley & Ben Powell

Production Team: Josh Pitt, Nicola Griffiths & Rob Beasley Spence

Executive Producers: Derek Muller & Casper Mebius

Additional video/photos supplied by Getty Images, Storyblocks

Music from Epidemic Sound