As a graph theorist, my primary interest here is whether those crossing arrows are necessary. We can ignore the directions on the arrows, obviously. We could el

As a graph theorist, my primary interest here is whether those crossing arrows are necessary. We can ignore the directions on the arrows, obviously. We could eliminate some crossings by moving ADC between Apple and LG. But the crossings involving the arrow from Oracle to Samsung are harder to get rid of ... [think, think, think] ... and, as it turns out, impossible to get rid of. To see this, begin by collapsing Nokia and Apple to a single node. Then Nokia-Apple, Kodak, and Sharp form a triangle, and Samsung is joined to each node in this triangle. Now collapse Rim, Motorola, Microsoft, Google, and Oracle to a single node. This new super-node is joined to all four of Nokia-Apple, Kodak, Sharp, and Samsung. Thus, we have a minor [1] isomorphic to a complete graph on 5 vertices. Conclusion: Considered as a graph, the diagram is not planar [2]. Crossings are unavoidable. Yes, I was bored, too. :-) P.S. Off-the-wall question: Are there any nontrivial graph-theoretic properties that such a graph might have, which also have nontrivial legal ramifications? [1] http://en.wikipedia.org/wiki/Minor_(graph_theory) http://en.wikipedia.org/wiki/Minor_(graph_theory) [2] http://en.wikipedia.org/wiki/Planar_graph http://en.wikipedia.org/wiki/Planar_graph