EdgeRenderingFunction is an option for GraphPlot and related functions that gives a function to generate the graphics primitives to use in rendering each edge.
EdgeRenderingFunction->g specifies that each edge should be rendered with the graphics primitives given by , where , are the beginning and ending points of the edge, , are the beginning and ending vertices, the is any label specified for the edge.
The graphics primitives obtained by applying EdgeRenderingFunction are in effect directly spliced into the graphic generated by a function like GraphPlot. Inset can be used to insert an arbitrary expression.