Unnecessary large white margin for graph with bezier curve

With the help from kglr (deleted comment):

Graphics[Show[Graph[{1 -> 1, 1 -> 1}]][[1]]]

which works by using Show to convert the graph to a Graphics[] object, and then constructing a new graphic using only the primitives and directives, but none of the options.

In this case PlotRangePadding is the option that causes the extra space, so using something like

Graph[{1 -> 1, 1 -> 1, 1 -> 1}, PlotRange -> 0]

or

Show[Graph[{1 -> 1, 1 -> 1}], PlotRangePadding -> None]

will only affect that particular option.

Another work around, adding a dummy vertex at the same coordinate seems to make things happy.

Graph[{1, 2}, {1 -> 1, 1 -> 1, 1 -> 1}, 
 VertexCoordinates -> {{0, 0}, {0, 0}}]

try also:

Graph[{1 -> 1, 1 -> 1, 1 -> 1}, PlotRange -> 0]