This is an option for the function monodromySolve which uses a complete graph. For instance, the user can choose to have 4 vertices and 2 edges connecting each pair of vertices. Then the homotopy will run on the complete graph on 4 vertices, where each edge is doubled.
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The object completeGraphInit is a function closure.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/MonodromySolver/Documentation.m2:646:0.