
396 Current Trends in Bayesian Methodology with Applications
FIGURE 19.1
Proximity graph for 100 vertices and radius r = 0.05.
proximity graph Prox(V, r) (see Figure 19.1) is formed by joining every pair
of (unordered) elements in V whose distance is 2r or less, i.e., whose c losed
balls of radius r intersect. As r range s from 0 to half the dia meter of A, the
graph Prox(V, r) ranges from the totally disconnected graph to the complete
graph. This example is a particular case of a more general construction where
hypergraphs can be computed from prop e rties of intersections of cla sses of
convex subs e ts in E uclidean space. The convex sets we consider ...