--------------------------------------------------------------------------------
No compression:

3 C1 + 2 C2 + 2 C3 + 9 OV; #graphs=12043, #rels=12019, time=6164.98
DimB[8, {3, 2, 2}] = 24
MemoryUsed[8, {3, 2, 2}] = 25729168

--------------------------------------------------------------------------------
Compression to a string:

CompressGraph[g_Graph] := StringTake[
  StringReplace[ToString[g]," "->""],
  {7,-2}
]

UncompressGraph[s_String] := ToExpression[
  "Graph["~StringJoin~s~StringJoin~"]"
]

3 C1 + 2 C2 + 2 C3 + 9 OV; #graphs=12043, #rels=12019, time=9375.63
DimB[8, {3, 2, 2}] = 24
MemoryUsed[8, {3, 2, 2}] = 57231008

--------------------------------------------------------------------------------
Compression to a large integer:

SetupCompress[g_Graph] := ($CompressionKey = {
  g,
  Length[g]^(Range[Plus @@ Length /@ g]-1)
})

CompressGraph[g_Graph] := (Cases[g,_Integer,{2}]-1) . $CompressionKey[[2]]

UncompressGraph[c_Integer] := Block[
  {len=Length[$CompressionKey[[1]]], t=c, r},
  $CompressionKey[[1]] /. i_Integer :> (
    t=(t-(r=Mod[t,len]))/len;
    1+r
  )
]

3 C1 + 2 C2 + 2 C3 + 9 OV; #graphs=12043, #rels=12019, time=10706.5
DimB[8, {3, 2, 2}] = 24
MemoryUsed[8, {3, 2, 2}] = 11306128