Wolfram Demonstrations Project

Let

be a set of vertices chosen from a grid. Given a vertex

, let

be the closest neighbor to

and draw a circle with center

and radius

. Draw an edge between two vertices

and

if their circles intersect. In other words, connect

and

. This gives the sphere-of-influence graph for the given set of vertices.

References:

G. T. Toussaint, "A Graph-Theoretic Primal Sketch," Computational Morphology (G. T. Toussaint, ed.), Amsterdam: Elsevier, 1988 pp. 220–260.

M. J. Lipman, "Integer Realizations of Sphere-of-Influence Graphs," Congr. Numer., 91, 1991 pp. 63–70.

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Sphere-of-Influence Graphs