  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.
