The planar embedding of a planar graph with the simultaneous minimization of an objective function of graph edge lengths is considered. It is shown that the so-called force embedding of a planar graph dictates a distinctive placement of the graph vertices and edges. This placement is a rectilinear edge embedding in which there are no edge intersections and the quadratic objective function of the edge lengths equals its global minimum. The, effectively O(mn), algorithm for finding the force embedding of a planar graph, where m and n are the number of the graph edges and the number of the graph vertices respectively, is presented.
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