In examining Small World Networks, Barabasi and Albert (1999) found that the degree distribution of these networks had no slope, also known as cutoff value. Barabasi and Albert investigated these networks in conjunction with the ‘trending’ of the power law distribution. In this context, when there is no cutoff value a scale-free distribution occurs, Watts (2004) observed. For this reason, Barabasi and Albert (1999) coined this manifestation as a scale-free network.
This discovery advanced and changed the thoughts about the “Small World Effect” (Newman, Barabasi & Watts, 2006). That being said, the Small World Effect has mostly been applied to the network structure of actors, link structure of the WWW, and Power Grid in Western USA (Watts. 2004). Addition to this the power law distribution (tail) did not occur in the Power Grid Analysis.
In real-world networks the links between others were right-skewed with a ‘heavy tail’, which illustrates that only a small amount of the hubs were many times better connected than the average of the majority of the nodes (Barabasi & Albert. 1999).
Barabasi appended two mechanisms to the Small World Model. These are population growth and preferential attachment. Simon (1955) and Price (1980) were the first ones accountable for these attributions. Their research shows that a scale-free network grows over time as new people join the network. However, they have a preference to join already well-connected people in the network – it is all what motivates us to join. This then contributes to a scale-free network.
Moving forward with what we experience on the Internet and in today’s business, an increasing number of businesses (referring to their physical location) are disappearing. They have lost the competition with the Internet.
A good example is Barnes & Nobles bookstores. What we experience in bookstores is what we label as ‘scarcity’. This potentially distorts our economy; scarcity in inventory, people, distribution, and so on. By contrast, scarcity does not (or limited) exist on the Internet. There is unlimited distribution, inventory, and so on. The Internet has become an attractive network, which is timeless, 24/7 available, and caters to a divers audience. All these aspects are no longer pertaining to physical location. Among others, it is the attractiveness of the online network that has people join.
Concluding the Internet is a scale-free network. It strives on the notion of its attractiveness and features such as timeless and borderless accessibility; rather than speaking about individuals as nodes the Internet’s nodes are documents and links are URLs (Bianconi, 2001) Networks are not static. They continuously increase and delete nodes and vertices, and they grow on the basis of preferential linking (2001).
References:
Barabasi, A.L., & Albert, R. 1999. Emergence of scaling in random networks. Science vol. 286 pp. 509-12
Bianconi, G. & Barabasi, Al. 2001. Competition and multiscaling in evolving networks. EDP Sciences, vol. 54 pp. 436-442.
Watts, DJ. 2004. The “New” Science of Networks. Annual Review Sociology. Vol. 30, pp. 243-270
Newman, M., Barabasi, A-L & Watts, D.J. 2006. The Structure and Dynamics of Networks, Princeton University Press, Princeton
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