http://www.springerlink.com/content/4fjgx8c7m92nqe05/fulltext.pdf

Recent class discussion has focused on the idea that the social network of the world can be modeled as a “small world” in which any two individuals are connected by a surprisingly short path. The notion of “six degrees of separation” presented by Stanley Melgram’s famous experiment (as discussed in class) provides strong support for this idea. In her paper “The Small World Web” (hyperlinked above), author Lada A. Adamic proposes the idea that the Web can be similarly modeled. Observing the Web on the “site level,” that is, treating a multi-page conglomerate such as www.amazon.com as a single node, Adamic notes that the Web is organized into a multitude of strongly connected clusters, which are more sparsely connected to other such clusters across the Web. For example, a search for “Republican Party” returns a large number of websites referencing the Party, and in most cases, referencing each other. These sites form a cluster, in which any given site in the cluster is connected to any other site in the cluster by a short path. However, it is less likely that there will exist a short path between a site for the Republican Party and, say, an online dating website, as they exist in two different clusters. This is analogous in some ways to the Watts - Strogatz model discussed in class, in that the websites forming a cluster create the densely connected network within a short distance of a given node and the sparser links between clusters correlates with the random “long-distance” links in the model.

There are several problems with representing the Web in this manner. In the Watts - Strogatz model, it was assumed that any two nodes within a given distance of one another on the grid share an edge. However, since the Web has no “distance” in the spatial sense, the assignment of a critical proximity (within which all nodes are connected) is more difficult. For example, one might note that two similar sites (for example, www.amazon.com and www.barnesandnoble.com) share a topic (in this case, book sales) and hence should be connected in a cluster. Common sense dictates that this is not the case, since there is no motivation for Barnes and Noble to direct potential customers to the website of a competitor (and vice versa). So, these two sites are not directly connected, but may still be connected by a short path (the proverbial “six degrees” ) should both sites be referenced on a third page (perhaps a catalog of reliable online booksellers), thereby preserving the “small world” nature of the cluster.