Small World Theory of the Web

What is the small world theory of the Web?

In the "small world" theory of the Web, every Web page is thought to be separated from any other Web page by an average of about 19 clicks. In 1968, sociologist Stanley Milgram invented small-world theory for social networks by noting that every human was separated from any other human by only six degrees of separation. On the Web, the small world theory was supported by early research on a small sampling of Web sites.

What is the significance of the "bow-tie" form of the Web?

The researchers discovered that the Web was not like a spider web at all, but rather like a bow tie (see figure below). The bow-tie Web had a "strongly connected component" (SCC) composed of about 56 million Web pages. On the right side of the bow tie was a set of 44 million OUT pages that you could get to from the center, but could not return to the center from. Finally, there were 16 million pages totally disconnected from everything.

Why does Barabasi call the Web a "scale free network" with "very connected super nodes"?

Barabasi's team found that far from being a random, exponentially exploding network of 8 billion Web pages, activity on the Web was actually highly concentrated in "very connected super nodes" that provided the connectivity to less well-connected nodes. Barabasi dubbed this type of network a "scale-free" network and found parallels in the growth of cancers, disease transmission, and computer viruses. As its turns out, scale-free" networks are highly vulnerable to destruction. Destroy their super nodes and transmission of messages breaks down rapidly.