The trading community is buzzing with the rumor that the upcoming Star Wars movie will offer a glimpse of the capital markets that finance the Galactic Empire's expansion. Due to the complete lack of natural topography, any location on the planet is equally likely to be the site of a dealer's post.
Dealers trade with each other by dispatching order-carrying robots.
Trading electronically would be much more efficient, but that would leave the Hollywood special effects wizards with little to depict. Consider the post of Dealer A, who is sending out his robots in random directions in search of counterparties. The effect of this rule is that one dealer will trade with another if and only if a robot traveling directly between them would never find itself closer to a third dealer than to the closer of the two. Each dealer trades with several other dealers, the exact number of which depends on how the posts happen to be arranged in his neighborhood. You may assume that the average distance between dealers is much smaller than the size of the planet, so that the curvature of the planet may be neglected.