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The first comment of
explains that the complement graph looks wrong only because it is plotted with the same layout as the original graph, so its edges are all horizontal, drawn on top of each other, making the drawing misleading (it looks as though many edges are missing).
To see the structure of the complement better, change the layout:
sage: G = graphs.CompleteBipartiteGraph(5, 6)
sage: G.show()
sage: Gc = G.complement()
sage: Gc.show(layout='spring')
