Web Graph Parameters and the Pagerank Distribution

Originally created for Web ranking, PageRank has become a major method for evaluating popularity of nodes in information networks. Besides its primary application in search engines, PageRank is successfully used for solving other important problems such as graph partitioning [3], spam detection [8], and finding gems in scientific citations [6], just to name a few. The PageRank [5] is defined as a stationary distribution of a random walk on the Web graph. At each step, with probability c, the random walk follows a randomly chosen outgoing link, and with probability 1− c, the walk starts afresh from a page chosen at random according to some distribution f . Such random jump also occurs if a page is dangling, i.e. it does not have outgoing links. In the original definition, the teleportation distribution f is uniform over all Web pages. Then the PageRank values satisfy the equation