Suppose that you are navigating in ``hyperspace'' and you have reached a web page with several outgoing links you could choose to follow. Which link should you choose in such an online scenario? When you are not sure where the information you require resides, you will initiate a navigation session. This involves pruning some of the links and following one of the others, where more pruning is likely to happen the deeper you navigate. In terms of decision making, the utility of navigation diminishes with distance until finally the utility drops to zero and the session is terminated. Under this model of navigation, we call the number of nodes that are available after pruning, for browsing within a session, the {\em potential gain} of the starting web page. Thus the parameters that effect the potential gain are the local branching factor with respect to the starting web page and the discount factor. 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 {\em erf} function. We derive an approximation to the potential gain of a web page and show that this is numerically a very accurate estimate. 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 it helps the user to choose a good starting point for initiating a navigation session. Another application is in social network analysis, where the potential gain could provide a novel measure of centrality.

12 pages, 3 figures, 1 table