Figure 3. Schematic representation of the structural discontinuity effect.

(a) In the classic gravity model, the probability p that two people communicate is a continuous (e.g. exponential) function of the distance between them. (b) In our hierarchy model, that probability is a discontinuous function induced by the assumption of a constant damping value q independent of the point of origin and the hierarchy level h. In both cases, the left panel shows in grayscale the probability of communication from a given point in space in a schematic country, partitioned in three regional levels with the same color coding as Fig. 1. The link between the borders and the deterrence function is clearly apparent in the second case.