13.1 It’s a small world after all

• Real-world social networks tend to be “small worlds”.

• In a small world architecture nodes belong to well defined clusters that are connected to one another.

  • Pairs exhibit few long paths and many short paths facilitated by hubs.

  • Highly clustered though proximal on average.

• “Six degrees of separation” https://www.sixdegreesofwikipedia.com/

• An extreme network structure is “caveman structure” of very tight and small clusters loosely connected to one another.

  

  A cave man structure of 100 people and 20 communites

  • Low density (connected edges out of all possible edges)

  • High transitivity (clustering tendency)

  • High path length AKA degrees of separation (>10) (average number of edges connecting two random nodes)

  • Large diameter (shortest path between two furthest nodes/ number of edges separate any two nodes on average).

How can one decrease the average path length of the caveman network? In other words, how to obtain a “small world” starting from a “cave man”? Bring it closer to a “random network”!

Randomly rewiring the network while maintaining the average node degree results is edges that cut through the network!

The more random rewiring the more similar it gets to a random network.

How does small world networks compare to other structures?

Neal, Z. (2018).

Watts, D., Strogatz, S. Nature (1998)