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I have made an animated graph that shows the changes of certain functions in time with different vertex sizes and colors:

gr = TreeGraph[RandomInteger[#] <-> # + 1 & /@ Range[0, 30], 
   VertexSize -> 0];

Manipulate[
 Show[{SetProperty[
    gr, {VertexSize -> 
      Table[ii -> 0.4 Sin[ii tstep]^2, {ii, VertexList[gr]}], 
     VertexStyle -> 
      Table[ii -> ColorData["Rainbow"][Cos[ii tstep]^2], {ii, 
        VertexList[gr]}]}], 
   Graphics[
    Text[Style[StringJoin["T=" , ToString[tstep]], Bold, 20], 
     Scaled[{0, 1}]], ImageSize -> {250, 100}]}], {tstep, 0, 5, 0.1}]

A sample result looks like this:

How can I add a legend to show the scale of vertex sizes and colors?

I have made an animated graph that shows the changes of certain functions in time with different vertex sizes and colors:

gr = TreeGraph[RandomInteger[#] <-> # + 1 & /@ Range[0, 30], 
   VertexSize -> 0];

Manipulate[
 Show[{SetProperty[
    gr, {VertexSize -> 
      Table[ii -> 0.4 Sin[ii tstep]^2, {ii, VertexList[gr]}], 
     VertexStyle -> 
      Table[ii -> ColorData["Rainbow"][Cos[ii tstep]^2], {ii, 
        VertexList[gr]}]}], 
   Graphics[
    Text[Style[StringJoin["T=" , ToString[tstep]], Bold, 20], 
     Scaled[{0, 1}]], ImageSize -> {250, 100}]}], {tstep, 0, 5, 0.1}]

A sample result looks like this:

How can I add a legend to show the scale of vertex sizes and colors? The closest solution I found was this one but I don't know how to implement the scaling part for what's shown in the legend to follow the style of the graph nodes.