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What use are graph duals?

While they can be formed and perceived to be "complements", then I have some difficulties in seeing what one needs them for.

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    $\begingroup$ Wikipedia has a nice page on Dual Graphs, perhaps you should start there. $\endgroup$ – Omnomnomnom Aug 8 '18 at 17:51
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    $\begingroup$ One very useful application is the proof of the Poincare duality Theorem in algebraic topology. $\endgroup$ – Arnaud Mortier Aug 8 '18 at 17:53
  • $\begingroup$ @Omnomnomnom Oh by that it would seem that the application of duals is similar to that in functional analysis. That by knowing that two spaces are dual to each other it might be easier to prove results on the other and then transform the results to the dual using the dual correspondence. $\endgroup$ – mavavilj Aug 8 '18 at 18:26

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