Webgraph

The webgraph describes the directed links between pages of the World Wide Web. A graph, in general, consists of several vertices, some pairs connected by edges. In a directed graph, edges are directed lines or arcs. The webgraph is a directed graph, whose vertices correspond to the pages of the WWW, and a directed edge connects page X to page Y if there exists a hyperlink on page X, referring to page Y.^[1]

Properties

• The degree distribution of the webgraph strongly differs from the degree distribution of the classical random graph model, the Erdős–Rényi model:^[2] in the Erdős–Rényi model, there are very few large degree nodes, relative to the webgraph's degree distribution. The precise distribution is unclear,^[3] however: it is relatively well described by a lognormal distribution, as well as the Barabási–Albert model for power laws.^[4][5]
• The webgraph is an example of a scale-free network.

Applications

The webgraph is used for:

• computing the PageRank^[6] of the world wide web's pages;
• computing the personalized PageRank;^[7]
• detecting webpages of similar topics, through graph-theoretical properties only, like co-citation;^[8]
• and identifying hubs and authorities in the web for HITS algorithm.