"Everyone knows the small-world phenomenon: soon after meeting a stranger, we are surprised to discover that we have a mutual friend, or we are connected through a short chain of acquaintances. In his book, Duncan Watts uses this intriguing phenomenon--colloquially called "six degrees of separation"--as a prelude to a more general exploration: under what conditions can a small world arise in any kind of network?

The networks of this story are everywhere [...]

How do such networks matter? Simply put, local actions can have global consequences, and the relationship between local and global dynamics depends critically on the network's structure. [...]