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Small world phenomenon

Milgram, Stanley. "The small world problem." Psychology today 2, no. 1 (1967): 60-67.

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Milgram’s Experiment

Milgram, Stanley. "The small world problem." Psychology today 2, no. 1 (1967): 60-67.

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Milgram’s Experiment Repeated

Dodds, Peter Sheridan, Roby Muhamad, and Duncan J. Watts. "An experimental study of search in global social networks." science 301, no. 5634 (2003): 827-829.

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Transitivity

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Clustering

Local clustering coefficient (Watts and Strogatz 1998)

Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.

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Local clustering coefficient (Watts and Strogatz 1998)

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Average Path Length

Average Path Length refers to the average distance between any two nodes in a graph. It is a measure that helps to understand the structure and connectivity of the graph

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Small World Phenomenon: Watts and Strogatz Model

Reconciling two observations:

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  1. High clustering: my friends’ friends tend to be my friends
  2. Short average paths

Watts, Duncan J., and Steven H. Strogatz. "Collective dynamics of ‘small-world’networks." Nature 393.6684 (1998): 440-442.

https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch20.pdf

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  1. Sporns, Olaf, Giulio Tononi, and Rolf Kötter. "The human connectome: a structural description of the human brain." PLoS Comput Biol 1.4 (2005): e42.
  2. Seung, Sebastian. Connectome: How the brain's wiring makes us who we are. HMH, 2012.
  3. Bassett, Danielle S., and Olaf Sporns. “Network neuroscience.” Nature neuroscience 20.3 (2017): 353-364.
  4. Fornito, Alex, Andrew Zalesky, and Michael Breakspear. "The connectomics of brain disorders." Nature Reviews Neuroscience 16.3 (2015): 159-172.

Network Neuroscience

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Bassett, Danielle S., and Olaf Sporns. "Network neuroscience." Nature neuroscience 20, no. 3 (2017): 353-364.