Generate an indexed set of random points.

points = Table[{i, RandomInteger[{1, 10}],  RandomInteger[{1, 10}]}, {i, 10}]
{{1, 3, 7}, {2, 3, 2}, {3, 7, 3}, {4, 4, 4}, {5, 3, 10}, {6, 3, 10}, {7, 9, 2}, {8, 8, 1}, {9, 2, 9}, {10, 8, 7}}

Here is a routine to plot a point:

pointPlot[{index_, x_, y_}] := {Circle[{x, y}, Offset[8]], Text[index, {x, y}]}

Here is a plot:

Graphics[{pointPlot /@ points},
 PlotRange -> All,
 PlotRangePadding -> 1/2,
 Frame -> True,
 ImageSize -> 300]

Offset specifies a size for the Circle in printers points so it will not be affected by AspectRatio. You could embellish the representation in various ways. Perhaps modify the routine to only require the index values. I'll leave it to you to write a routine to draw a line between specific points.