Modelling the navigation potential of a web page

Navigating the web involves pruning (or discounting) some of the outgoing links and following one of the others. More pruning is likely to happen for deeper navigation. Under this model of navigation, we call the number of nodes that are available after pruning, for browsing within a session, the potential gain of the starting web page. We first consider the case when the discounting factor is geometric. We show that the distribution of the effective number of links that the user can follow at each navigation step after pruning, i.e. the number of nodes added to the potential gain at that step, is given by the erf function, which is related to the probability density function for the Normal distribution. We derive an approximation to the potential gain of a web page and show numerically that it is very accurate; we also obtain lower and upper bounds. We then consider a harmonic discounting factor and show that, in this case, the potential gain at each step is closely related to the probability density function for the Poisson distribution. The potential gain has been applied to web navigation where, given no other information, it helps the user to choose a good starting point for initiating a "surfing" session. Another application is in social network analysis, where the potential gain could provide a novel measure of centrality. (C) 2008 Elsevier B.V. All rights reserved.