FIRST EDITIONS IN ORIGINAL WRAPS OF MILGRAM’S TWO LANDMARK ‘SMALL-WORLD PROBLEM’ PAPERS & A COLLECTION OF SEVEN MORE SEMINAL PAPERS ON THE SMALL-WORLD PROBLEM – also known as six degrees of separation.
“In 1967, social psychologist Stanley Milgram conducted a seminal experiment to test the hypothesis that scattered members of any large social network (here, the United States) could be connected to each other through short chains of intermediate acquaintances” (Levinson, Village, I, 1255). Milgram put it this way: “The simplest way of formulating the small-world problem is: Starting with any two people in the world, what is the probability that they know each other?” (Milgram, 62).
To find out, he “mailed a passport-like packet to a few hundred randomly selected individuals in Nebraska and Kansas, explaining that the packet’s final destination was one of two target recipients in the Boston area. Milgram instructed his subjects to send the packet… to someone whom they knew on a first-name basis – someone they thought was more likely to be acquainted with the target person than they were themselves…
“His famous result, now enshrined in popular culture and sociology dogma, was that the average length of the resulting acquaintance chains was roughly six links, where the final member of the chain was the target itself. This result led to the phrase ‘six degrees of separation’”, [though Milgram never used it] and later Guare’s play of the same name (Levinson).
Two Granovetter papers build on Milgram and are among the most important in the social sciences. His ‘Strength of Weak Ties’ are pioneering, highly influential papers arguing that “In marketing, information science, or politics, weak ties enable reaching populations and audiences that are not accessible via strong ties” (Wikipedia). Granovetter concludes “that no strong tie is a bridge, and therefore “all bridges are weak ties” (Granovetter, 1363). Weak ties, he argues, “are more likely to link members of different groups in networks than strong ones. Weak ties connect different actors and consequently enable the flow of information” (Trost, Social Media, 17).
Kochen and de Sola Pool formally and famously articulate “the mechanics of social networks and explore the mathematical consequences of these (including connectedness)” (Wikipedia). Their work "provided the intellectual impetus for a whole generation of students who designed and executed studies of the 'small-world'."
In 1998 Watts and Strogatz seminally document the best known family of small-world networks and posit the network model as a framework to study the small-world problem. Their work "provided compelling evidence that the small-world phenomenon is pervasive in a range of networks arising in nature and technology, and a fundamental ingredient in the evolution of the WWW” (Kleinberg, 1).
Brabási and Réka introduce an algorithm used to generate random, scale-free networks. Scale-free networks are often observed in natural as well as human created systems, including cellular networks, the WWW, Internet, and social networks.
Kleinberg's 2000 paper rigorously quantifies the small-world network . Kleinberg first recognized that Milgram’s small-world implicitly argues not only the presence of short paths between “individuals in social networks, but also that people seem to be good at finding those paths, an apparently simple observation that turns out to have profound implications for the structure of the networks” (Wikipedia). Lastly, the play Six Degrees of Separation is included for a bit of fun. Item #605
DETAILS: All papers housed in individually-sized compartments in a handsome leather and cloth clamshell case. Kleinberg’s paper is a bound extraction; Granovetter’s second paper is bound and includes dust cover; Strogatz’s paper is inscribed. All others are journal issues in original wraps. Mailing labels appear on most; a few are ex-libris; withal, the collection is in fine condition.