Vertex Labels at wrong positions after exporting?

I have a graph with a large number of vertices. Mathematica can handle it nicely:

However, when I leftclick and “save graph as” and save it as PDF the labels appear below the vertices and is looks pretty bad. The same happens when I

Export["path", graph, "PDF" ];

It looks like this:

Why are the vertex labels at a different Position after Exporting? Even with

VertexLabels -> Placed [Automatic , {0.5, 2} ]

after Exporting, the labels appear on the same position below the vertex (instead of above the vertex as in Mathematica). Is there something I can do?

I don’t know about eps, but the export to pdf changed a lot with version 12.1 and it introduced a lot of bugs. It also removed the functionality of exporting Graphics3D to vector pdf. To make pdf of pictures I am forced to revert to 12.0.