ABSTRACT
The World Wide Web (WWW) network is the biggest example of providing topological information. Its nodes are the documents (web pages) and its edges are the hyperlinks (URL) connecting one document to another. The interest in the WWW as a network simply exploded after discovering that the distribution of the degrees of the Web pages is given by a power law over several magnitudes (Barabási et al. 1999). Moreover, the cited work, supplemented and developed in Albert and Barabási (2002) paved the way for extensive research based on rigorous mathematical models. Because the edges of the WWW graph are directed, the network is dened by a two-degree distribution: output arcs’ degree Pout(k), which
is the probability for a document to have k URL links to other documents, and the input arcs’ degree Pin(k), which is the probability that k URL link to indicate to a certain document. Several studies reported that both Pout(k) and Pin(k) have power law queues:
P k k P k kout in out inand( ) ( )∼ ∼− −γ γ (4.1)
Albert, Jeong, and Barabási (2000) studied a subset of the WWW containing 325,729 nodes and found that γout = 2.45 and γin = 2.1. Other researchers used a slightly different representation of the WWW, treating every node as a domain name and considering that any two nodes are connected if a page from one refers to a page in the other. Although this method often associates thousands of pages belonging to the same domain, being a nontrivial node aggregation, the distribution of the outgoing arcs still follows a power law equal to γ indom = 1 94. .
