Search Parameters for the Small World Problem

In "small world" studies successive men each send on a postcard packet to an acquaintance who may know a designated target person on a first-name basis. In this analysis the likelihood of discarding the packet is separated from the chance the packet if sent reaches a man who knows the target. The former probability is assumed to be independent of the previous number of persons in the chain. The assumption is satisfied by the three extant sets of aggregate data. Then the latter probability is found to rise from zero to a modest plateau with the number of steps in the chain. Refinements and variants of the model are suggested. Funneling of chains through a few persons near the target is discussed. Social processes shape and are shaped by 1966). Snowballing effects however make it networks of particular ties linking individvery difficult to trace networks through many uals in populations. Even in the field of links; so the long-range structure and intermass media Katz and Lazarsfeld (1955) 1oi:g locking of such networks in large population~ ago emphasized this truth as a balance to remains unclear. Rapoport and Horvath conventional pictures of attitudes being broad(1961) extended classical sociometry to larger cast direct to categories of people. Studies of groups and provide some insight into condiffusion-of rumors, fads, disease, or innonectivity properties. A second empirical apvations-were a natural first approach to the proach to networks has focused on how links empirical study of networks (Coleman et al., of different affective quality tend to fit together in balanced groupings among small sets af * Stanley Milgram suggested this analysis and I people (e.g., Bott, 1957; White, 1961)am indebted to him, Jeff Travers and Charles again the overall topology of networks remains Korte for explainhi their ideas and data. Financial support was received from ?he National obscure, although ties are made between netScience Foundation under Grant GS-448. work study and classical ideas of role theory.