Let be a set of vertices chosen from a grid. Given a vertex in , let be the closest neighbor to in and draw a circle with center and radius . Draw an edge between two vertices and if their circles intersect. In other words, connect and if . This gives the sphere-of-influence graph for the given set of vertices.
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.