Draw a graph with zero-size vertices

Questions
,
1

How can I draw only the edges of a graph but not the vertices?

I am looking for something like

RandomGraph[{10, 20}, VertexShapeFunction -> None]

but the edges should start and end precisely in the vertex coordinate. There should be no space left for a vertex. If there a way through Graph, and not manually constructing it using Graphics?

Screenshot2015-10-0515.21.17
Screenshot2015-10-0515.21.17774×706 42.6 KB

2

By default the edges are “foreshortened”. You get full edges with an appropriate EdgeShapeFunction, for example

RandomGraph[{10, 20}, EdgeShapeFunction -> (Line[#1] &), 
 VertexShapeFunction -> None]
3

Thank you, I didn’t realize that it was the edge shape function doing it.