In this paper, we put two concepts together: Shortest paths and starant graphs. We calculate the costs involved in putting two randomly selected individuals in contact in a controlled network. That would be the costs in terms of public health. Disease spread became our main concern in what comes to the starant graphs in the year of 2002 because that is one of the directions the work of Comellas et al. and Watts et al. pointed at, and our work is inspired in theirs. Other factors, such as random, and unexpected, contact between individuals, are disregarded, so that if the individual visits the clinic that belongs to Mister X, his mate, but his usual doctor, Mister Y, is not there, and he is then served by Miss R, we will need new calculations, what means that we go from predictive power to disgrace power, and that frontally opposes our initial intentions with this work.
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