What is the probability threshold for including an edge using the Waxman model?

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I came across a paper describing how it builds a graph based on the Waxman model (link to the probability function Waxman gives) but I was wondering what the probability threshold is for determining if an edge exists between two nodes. Is it strictly a binary yes or no in terms of whether an edge exists, and if so, at what probability do we decide this is the case? The paper I am reading does not specify one of its own and upon some preliminary reading I cannot seem to find this either. Or would it be more accurate to consider it as only giving some percentage of an edge between the nodes, if that makes sense.

Thanks for any help.