nodeList = {a, b, c};
edgeList = {a <-> b, b <-> c, c <-> a};
aShape = ToExpression["$c=\sqrt{a^2+b^2}$", TeXForm, HoldForm];
bShape = ToExpression["$c=\sqrt{b^2+a^2}$", TeXForm, HoldForm];
cShape = ToExpression["$\text{Area equals A}$", TeXForm, HoldForm];
Print["The 3 labels are: ", {aShape, bShape, cShape}];
shapeList = {a -> aShape, b -> bShape, c -> cShape};
g = Graph[nodeList, edgeList, VertexShape -> shapeList, VertexSize -> Large]

asc = <|a -> aShape, b -> bShape, c -> cShape|>

Graph[nodeList, edgeList,
 VertexShapeFunction -> (Inset[Framed@StandardForm@asc[#2], #1] &),
 PerformanceGoal -> "Quality",
 VertexStyle -> Black
]

<<IGraphM`
IGExpressionTree[First@Roots[x^2 + a x + 1 == 0, x],
   VertexLabels -> "Subexpression",
   PerformanceGoal -> "Quality",
   ImageSize -> 280
   ] //
  IGVertexMap[
   Function[e, Inset[Panel[e], #1] &],
   VertexShapeFunction -> IGVertexProp[VertexLabels]
   ] // RemoveProperty[#, VertexLabels] &

a = "c=\sqrt{a^2+b^2}";
b = "c=\sqrt{b^2+a^2}";
c = "\text{Area equals A}";

<< MaTeX`

Graph[{a <-> b, b <-> c, c <-> a},
 VertexShapeFunction ->
  Function[{position, vertex, size}, Inset[Framed[MaTeX[vertex], FrameStyle -> None], position]],
 PerformanceGoal -> "Quality"
]