simpleGraph = {1 [DirectedEdge] 2, 2 [DirectedEdge] 3, 3 [DirectedEdge] 1, 1 [DirectedEdge] 4, 4 [DirectedEdge] 2};

Graph[simpleGraph, VertexLabels -> "Name"]

Graph[simpleGraph, VertexLabels -> Placed["Name", Above]]

Graph[simpleGraph, VertexLabels -> Callout["Name", Above]]

Graph[{1 [DirectedEdge] 2, 2 [DirectedEdge] 3, 3 [DirectedEdge] 1, 1 [DirectedEdge] 4, 4 [DirectedEdge] 2}, VertexLabels -> Callout[{1, 2, 3, 4}, {1, 2, 3, 4}, Above]]

exampleGraph={17835 [DirectedEdge] 17848, 17848 [DirectedEdge] 20967,
 17835 [DirectedEdge] 17845, 17845 [DirectedEdge] 20967,
 17835 [DirectedEdge] 5779, 5779 [DirectedEdge] 20967,
 17835 [DirectedEdge] 3931, 3931 [DirectedEdge] 20967,
 17835 [DirectedEdge] 3870, 3870 [DirectedEdge] 20967,
 17835 [DirectedEdge] 3554, 3554 [DirectedEdge] 20967,
 17835 [DirectedEdge] 3403, 3403 [DirectedEdge] 20967,
 20967 [DirectedEdge] 12657, 12657 [DirectedEdge] 17835,
 20967 [DirectedEdge] 9038, 9038 [DirectedEdge] 17835,
 20967 [DirectedEdge] 5779, 5779 [DirectedEdge] 17835,
 20967 [DirectedEdge] 3870, 3870 [DirectedEdge] 17835,
 20967 [DirectedEdge] 3637, 3637 [DirectedEdge] 17835,
 20967 [DirectedEdge] 3554, 3554 [DirectedEdge] 17835,
 20967 [DirectedEdge] 3367, 3367 [DirectedEdge] 17835,
 20967 [DirectedEdge] 1390, 1390 [DirectedEdge] 17835,
 20967 [DirectedEdge] 560, 560 [DirectedEdge] 17835,
 20967 [DirectedEdge] 482, 482 [DirectedEdge] 17835};

getVerticies[edgeList_] := Module[{vertexList = {}},
  Table[AppendTo[
    vertexList, {edgeList[[i]][[1]], edgeList[[i]][[2]]}], {i, 1,
    Length[edgeList]}];
  Return[DeleteDuplicates[Flatten[vertexList]]]
  ]
makeVertexLabels[vertexList_, labelList_] :=
  Return[Table[
    vertexList[[i]] -> Placed[labelList[[i]], Center], {i, 1,
     Length[vertexList]}]];
makeEdgeLabels[edgeList_, labelList_] :=
  Return[Table[
    edgeList[[i]] -> Placed[labelList[[i]], "Middle"], {i, 1,
     Length[edgeList]}]];

simpleGraph = {1 [DirectedEdge] 2, 2 [DirectedEdge] 3,
  3 [DirectedEdge] 1, 1 [DirectedEdge] 4, 4 [DirectedEdge] 2};
listOfVertexNames = {"One", "Fish", "Two", "Fish"};
listOfEdgeNames = {"Red", "Fish", "Blue", "Fish", "Octupus"};

Graph[simpleGraph,
 VertexLabels ->
  makeVertexLabels[getVerticies[simpleGraph],
   Range[Length[getVerticies[simpleGraph]]]],
 EdgeLabels ->
  makeEdgeLabels[simpleGraph, Range[Length[simpleGraph]]]]

verticies =
 Prepend[Table[
   Range[Length[getVerticies[simpleGraph]]][[i]] ->
    listOfVertexNames[[i]], {i, 1, Length[listOfVertexNames]}],
  "Verticies"]
edges = Prepend[
  Table[Range[Length[simpleGraph]][[i]] -> listOfEdgeNames[[i]], {i,
    1, Length[listOfEdgeNames]}], "Edges"]
Grid[{{Column[verticies]}, {Column[edges]}}, Alignment -> Left,
 BaselinePosition -> Top]

gr=Graph[exampleGraph];

lp=ListPlot[Callout@@@Transpose[{GraphEmbedding[gr], VertexList[gr]}],
Axes->False, PlotStyle->None];

Show[gr, lp]

Graph[exampleGraph, VertexLabels->"Name"]

Graph[exampleGraph, ImageSize -> 500, VertexShapeFunction -> "Name"]