Internet: Diameter of the World-Wide Web

By Réka Albert, Hawoong Jeong, Albert-László Barabási. 1999

Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the web's connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.

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Citations in the corpus

Community detection in graphs (2009, background): “In these cases, it is however important to have at least an estimate of the worst-case complexity of the algorithm, which is the amount of computational resources needed to run the algorithm in the most unfavorable case for a given system size.”
Graph evolution: Densification and shrinking diameters (2006, background): “The diameter is a slowly growing function of the network size, as in small world graphs [Albert et al. 1999; Broder et al. 2000b; Milgram 1967; Watts et al. 1998].”
Beyond Gaussian averages: redirecting international business and management research toward extreme events and power laws (2007, background): “…Alliance networks among biotech firms Italian industrial districts Transition economies Casti (1994) Zipf (1949); Abrams and Strogatz (2000) Albert et al. (1999) Faloutsos et al. (1999) Adamic and Huberman (2000) Dezsö et al. (2006) Aiello et al. (2000); Ebel et al. (2002) Watts (2003)…”
Structure and Dynamics of Networks (2009, background): “One of the most obvious and prominent examples is the Internet [Albert et al., 1999, Barabási & Albert, 1999, Pastor-Satorras & Vespignani, 2004].”
The Web as a graph (2000, background): “al.[2] predict that for most pairs of web pages u and v the directed distance (following hyperlinks) from u to v is about 19, a so-called small world phenomenon.”
Fashions, habits and changing preferences: Simulation of psychological factors affecting market dynamics (2001, unknown): “Despite about a billion of documents on the web, the average distance between documents was estimated only to be about 19 hyperlinks (Albert et al., 1999).”