Compare following two low-level box representations of a graph without VertexLabels and one with VertexLabels set to "Name" with ToBoxes[]:
ToBoxes[Graph[{1 <-> 2}]]
ToBoxes[Graph[{1 <-> 2}, VertexLabels -> "Name"]]
(Alternatively, select visual representation and press Cmd+Shift+E on mac.)
The first one uses GraphicsComplex for an efficient representation of the graph and the second does not.
Is there a conceptual or technical reason for this?
I came across this trying to use this answer for a graph with VertexLabels enabled where GraphicsComplexBox[x_, y_, z___] does not match anything anymore.
Mathematica version: 11.2

PropertyValuesforGraphsis handled quite differently than without (and often in an inconsistent way but that's another story). This is maybe because there can be so many exceptions... And usingVertexLabelsalso implies that your graph is not overly large so that the profit fromGraphicsComplexis marginal, right? Maybe that was the thinking behind this design decision... – Henrik Schumacher Apr 13 '18 at 17:34Normal[]or another function to get an identical representation for both? – Hotschke Apr 13 '18 at 17:44AdjacencyGraph@AdjacencyMatrixshould get rid of allPropertyValues. Plotting it leads to aGraphicsComplex, but the vertex lables, vertex coordinates, etc. are gone. Is that what you need? – Henrik Schumacher Apr 13 '18 at 18:37H = Graph[VertexList[G], EdgeList[G]]. Depending on the internal representation of the graph (sparse or not), the one or the other may be faster. – Henrik Schumacher Apr 13 '18 at 18:42displayWeightedMultiGraphshown in the mentioned answer to handle both situations. – Hotschke Apr 13 '18 at 18:50Block[{Identity}, Graph[{1 \[DirectedEdge] 1, 1 \[DirectedEdge] 1, 1 \[DirectedEdge] 1}, EdgeWeight -> Identity /@ {{1, 0}, {0, 1}, {1, 1}}, VertexLabels -> "Name", EdgeLabels -> "EdgeWeight" ] ]. – Henrik Schumacher Apr 13 '18 at 19:50EdgeLabels -> "EdgeWeight", which resolves the display issue? – Henrik Schumacher Apr 13 '18 at 20:06Normal[Graph]does not work. The documentation sounds promising but again does not work here because the undocumentedGraphicsComplexBoxis used. – Hotschke Apr 13 '18 at 20:06