Weblog (4); Small World Theory & Searchability

Small World Theory & Searchability

In a desire to improve an individual’s standard of living one needs to examine the social network in which they partake and interact. This data provides them with insight on the quality of the network.
Individuals generally express their preferences for one individual over the other (or one network over another). It is this preferential attachment that elevates the growth of well-connected networks above weaker ones (Granovetter, 1973, Watts, 1999, 2003, 2004). The outcome is a scale-free network rather than a small world network, or generalized affiliated network, as illustrated by the work of Krapivsky, et al (2000) and Barabasi & Albert (1999).
Individuals connect on the premise that they share a common social dimension. The dynamics of social networks attempting to increase the standard of living greatly depends on the reciprocal value it supports for each individual. The social dimensions of the network, the social class, demographics and so forth determine whether an individual searches and connects to the ‘new’ network. This relation reflects the model of generalized affiliation networks of Watts (Watts, 2002, 2003).
The predisposed thought that adding random connections to a network could potentially ruin the network has been refuted by Watts and Strogatz’s (Watts, 1998) model. The model found that if an individual added a few random connections into a complex network, the individual could make the network both more efficient and effective. In fact, randomness could dramatically improve the performance of a complex system rather than ruining it (CBS Interactive, 2010).
Watts (2004) argued that this social network model should be extended to enable search-ability based on the fact that short paths existed between randomly depicted individuals on a local basis. The model enabled the use of local information to search for others; however, the model did not support the search-ability feature when searching for people or organizations foreign to the network. It was initially Milgram, and thereafter Kleinberg (Kleinberg, 2000a), that discovered and added the capability of searches outside a specific network to the network model of Watts & Strogatz (Watts, 2004). In fact, now one could search for information on a global scale instead of primarily on a local one.

References:

Barabasi, A.-L., Albert, R. 1999. Emergence of scaling in random networks. Science, 286, 509-12.

Bianconi, G., Barabasi, A.L. 2001. Competition and multiscaling in evolving networks. EDP Sciences, 54, 436-442.

CBS Interactive, C. 2010. Network theory's new math [Online]. Available: http://news.cnet.com/2009-1069-978596.html [Accessed 27 August 2010].

Kleinberg, J. 2000a. The small-world phenomenon: an algorithmic perspective. Proc. 32nd ACM Symphony Theory Computing, 32, 163-170.

Krapivsky, P. L., Redner, S. & Leyvraz, F. 2000. Connectivity of growing random networks. Phys. Rev. Lett, 85, 4629-32.

Watts, D. J. 1999. Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton, Princeton University Press.

Watts, D. J. 2001. A simple model of global cascades on random networks. PNAS, 99, 5766-5771.

Watts, D. J. 2002. A simple model of information cascades on random networks. Proc. Natl. Acad. Sci. USA, 99, 5766-71.

Watts, D. J. 2003. Six Degrees: The Science of a Connected Age, London, Vintage Books.

Watts, D. J. 2004. The “New” Science of Networks. Annual Review Sociology, 30, 243-270.

Watts, D. J., Strogatz, S.H. 1998. Collective dynamics of 'small-world' networks. Nature, 393.