Graph vs. GraphPlot

Question

What is the difference (in purpose) between Graph and GraphPlot? Which function is bested suited to which tasks?

Background: I just spent the last two hours trying to make this graph readable:

trans = Uncompress@
   "1:eJyVV01vwjAMRfu47U/sv3RKKc2KGsahxw2YOE0aXPff17RJSZD8/HIBga3Efn5+\
dl4/f/rT32q1ujyNH+35cj09+F8v40d1/j1+XY+\
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ORPLDl/FENXLXCmuVWQanrkBwmT88uGjhh8JgIyYRI91EW4aBoqtOIbg60RxD+IAGjuZC+\
QRSeXfC2qkhGor6gqD60WfdoZTOy8SGu9iONKFEJeVO7eELQGMvOD0UDYaXHN5a6DT5Zlv\
GuYlu2TmhIyD726bP5gSnswmEttWR9puG1wH6WE1VuSBI2sVNA6cfxlK6JIx7utFDE7vI5\
lyAL+Kv09FopgpA9t+\
cIcCcjZMXgYV4YWrHd86DFyR2xpTh012aCEY8sSoy3sX3A0OHUHTjWYWgR8fv/wd/kB";
Graph[DeleteDuplicates@trans, VertexLabels -> Placed["Name", Center], 
 VertexShapeFunction -> "Capsule", VertexSize -> 1, 
 VertexLabelStyle -> Large, 
 EdgeShapeFunction -> 
  GraphElementData["ShortUnfilledArrow", "ArrowSize" -> 0.02]]

Then I discovered that GraphPlot produces much more readable results:

GraphPlot[
 DeleteDuplicates@trans /. (DirectedEdge[a_, b_] -> Rule[a, b]), 
 VertexLabeling -> True, DirectedEdges -> True]

which prompted me to wonder: what's the point of Graph?

Of course I noticed this, while related, which asks about the Combinatorica package.

Answer 1

First of all Graph is more recent functionality. Now try this:

GraphPlot[{1 -> 2}] // Head

Graphics

and then this

Graph[{1 -> 2}] // Head

Graph

Basically while GraphPlot and GraphPlot3D both return pure graphic objects, Graph returns true graph which contains all information about the graph and can be computed with. For example:

g=Graph[{1->2}];
 AdjacencyMatrix[g] // Normal

{{0, 1}, {0, 0}}

Because they can be computed with, there is wide functionality built around Graph objects which GraphPlot does not have - from graph theory to visualization and styling.

Also to get more feel for the difference you can try AtomQ, which is the function that yields True if expression cannot be divided into subexpressions, and yields False otherwise, - as paraphrased from form Documentation Center.

AtomQ[g]

True

Compare with

 AtomQ[GraphPlot[{1 -> 2}]]

False

Which can be also hinted from:

 g // InputForm

Graph[{1, 2}, {DirectedEdge[1, 2]}]

and this:

 GraphPlot[{1 -> 2}] // InputForm

Graphics[Annotation[GraphicsComplex[{{1., 0.}, {0., 8.979318433952318*^-11}}, {{RGBColor[0.5, 0., 0.], Line[{{1, 2}}]}, {RGBColor[0, 0, 0.7], Tooltip[Point1, 1], Tooltip[Point2, 2]}}, {}], VertexCoordinateRules -> {{1., 0.}, {0., 8.979318433952318*^-11}}], FrameTicks -> None, PlotRange -> All, PlotRangePadding -> Scaled[0.1], AspectRatio -> Automatic]

Good thing to know is that built-in GraphData return Graph object on default:

GraphData /@ GraphData["Hypotraceable"]

And another cool consequence of the above is that you can even copy and paste the visual representations returned by Graph and compute them:

Besides GraphData there are many other functions that return Graph objects, such as CompleteGraph, GraphComplement, CayleyGraph, Subgraph and so on.

Another thing to know is that Graph objects have their own right-click menu alowing one to deal with the graph interactively (sample workflow is shown below):

GraphData["IcosahedralGraph", "LineGraph"]