Small World

How Small Worlds Form

SWNs are noteworthy for three reasons. First, they are a particular class or category of networks. Second, SWNs have been a key research question historically and also in the more recent reemergence of broad and multidisciplinary interest in networks. Finally, SWNs, more than many network concepts, have a cultural relevance as a touchstone for understanding network dynamics and how they relate to contemporary life in a globalized information society.

A Hungarian writer, Frigyes Karinthy, first explored small world networks and six degrees of separation in a short story from 1929 titled Chains. The early sociograms [Page 785]of Jacob Moreno, an immigrant sociologist influenced by Georg Simmel, were one of the earliest efforts to formally study a network as an entity unto itself. The sociograms laid the groundwork for understanding how microprocesses could lead to macropatterns. Milgram and Jeffrey Travers in the 1960s set out to measure the average distance among people using the method of letters passing from sources to a target. The results, published in Psychology Today in 1967, became widely popular and even passed into cultural parlance as “six degrees of separation.” While Milgram's conclusions were based on scant evidence, the core insight had taken hold of structural properties due to the network. The meaning of small, or six degrees, became a key question as social scientists shifted to asking not about the existence of SWNs but how they function as a structure for action. One may be only three or four degrees from the president of the United States, but how does that matter? From the 1990s to the 2000s, the interest in the SWN problem percolated among a variety of scholars in other fields including mathematics, physics, computer science, information studies and most social sciences.

The new wave of interest discovered that SWNs are found in a variety of social and physical contexts. D. Watts, S. Strogatz, M. Newman, A. L. Barabási, and others also helped establish that SWNs are far more likely in most social contexts than any sort of planned or random network. The vibrant exchanges among the various fields interested in networks led to the conclusion that SWN can be defined as one where cohesion increases more quickly than average degree. Once the definition and ubiquity of SWNs was established, social scientists turned to how SWNs form, their resilience and evolution, and how they form the structural basis of activity in a variety of domains. The first way an SWN forms is through preferential attachment, also known as the Matthew Effect. This is also known as a scale-free network. The assumption is that a network grows as nodes are added and that new nodes are more likely to link to extant nodes of higher degree. Airports in a route network or pages on the Web are two examples of these scale-free, or hub-and-spoke, networks. Preferential attachment can shed light on traditional concerns about inequality or stratification. The second is through overlapping affiliations. Imagine a network of people, all of whom have multiple affiliations. While most have overlapping affiliations, a few will have nonoverlapping affiliations, meaning that they act as bridges or shortcuts among the whole network. The affiliation network is more recognizable to many social scientists since the affiliations, such as neighborhood, occupation, race, or other forms of community, are amenable to many other research paradigms.

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