The Small-World Phenomenon.

I picked an old printout at home and realized I had never gotten down to reading it. I took to reading it just now. The paper is on The Small-World Phenomenon: An Algorithmic Perspective by Jon Kleinberg.

It deals with the "six degrees of separation" concept of social networks.

"A social network exhibits the small-world phenomenon if, roughly speaking, any two individuals in the network are likely to be connected through a short sequence of intermediate acquaintances."

The paper starts of with two questions

1. Why should there exist short chains of acquaintances linking together arbitrary pairs of strangers?

Stanley Milgram's conducted experiments in this field in the 1960's. Over many trials, it was discovered that the average number of intermediate steps, linking two individuals, in a successful chain was found to lie between five and six, a quantity that has since entered popular culture as the ``six degrees of separation'' principle. Each link in the chain linked two people who knew each other on a first-name basis.

2. Why should arbitrary pairs of strangers be able to find short chains of acquaintances that link them together?

This question deals with the finding that people were be able to find these chains knowing so little about the target individual.

Further down the paper grew very mathematical - and to my shock - I left it aside. Some years ago (or should I say a decade?) I would have voraciously read many such mathematical papers ...