## An Experimental Study of the Small World Problem. Travers, Milgram. Sociometry 1969.

1. The famous “six degrees of separation paper”, where people were told to direct a letter to a particular individual, but by way of people they knew only on a first name basis
2. There were three groups of people in the study:
3. Random people in Boston
3. The target individual was a stock trader in Boston so those three groups are supposed to cover people who: have nothing in common with the target, share an occupation with the target (but are far away), and those who are physically near but do not share an occupation with the target
4. Other information given about the target was address, occupation, employer, college/year of graduation, military service dates, wife’s maiden name and hometown
5. People were supposed to list themselves as they sent the item so that an end count could be achieved as well as to prevent looping.  They were also supposed to send information about themselves to the authors
6. 217 of the 296 starting participants forwarded the letter to someone else
7. Chains had to be long because if they were too long eventually it would come across somebody who would stop forwarding
8. Ultimately, 29% (64) of the letters sent out by the initial group made it to the goal
9. Mean length was 5.2 links
10. The average length of paths starting from Nebraska was 6.1, from Boston was 4.6.  Analysis indicates that Usually 1 or 2 hops were needed to get a message from Nebraska to Boston, and then a similar trajectory occurred from there until a letter made it to an individual close (in terms of a personal relationship) to the target
11. There were 232 letters that did not make it through.  The distribution of length each letter took looks like what would be expected in a decay curve where each step had a probability of terminating (looks like that would be about 1/3 from the graph – good eye, its 27%).  The mean length of failed chains is 2.6 links
12. People may terminate a chain either because they are uninterested, or because they don’t know who to send it to next that could get it closer
1. In instances of the second case, the expected length of the chain if it was sent on would probably be larger than the mean value of those letters that did make it to the goal
13. From the cards, they do have some information about the dropouts, because people were asked to send information about the person they sent the package to, but they weren’t able to derive anything with statistical significance from that information
14. Difference in path lengths between those in Nebraska who were “random” or worked in the stock exchange didn’t have an influence on path length
15. As chains get closer and closer to target, more chains go through the same individuals
16. 25% of letters reached the target through a particular neighbor he had, 10% through one business associate, and 5% through another business associate.  About half of the successful chains went through one of these three people
17. “Data on patterns of age, sex, and occupation support the plausible hypothesis that participants select recipients from a pool of individuals similar to themselves. The data on age support the hypothesis unequivocally; the data on sex and occupation are complicated by the characteristics of the target and the special recruitment of establishing contact with him.”  These generally matched (with p<0.001) between sender and receiver