A[G_Graph]:=Normal[AdjacencyMatrix[G]];
DMat[G_Graph]:=DiagonalMatrix@VertexDegree[G];
FindDegSimMat[G1_Graph,G2_Graph]:=Module[{n=VertexCount[G1],M},If[n!=VertexCount[G2],Abort[]];M=Array[(Subscript[m, #1,#2])&,{n,n}];M=M/.Solve[{A[G1].M==M.A[G2],DMat[G1].M==M.DMat[G2]}][[1]]];
FindDegSimMat[list_List]:=FindDegSimMat@@@Subsets[list,{2}];
FindDegSimMatDet[G1_Graph,G2_Graph]:=Det[FindDegSimMat[G1,G2]];
FindDegSimMatDet[list_List]:=FindDegSimMatDet@@@Subsets[list,{2}];
matrixRowSumQ=Not[MemberQ[Total/@#,0]]&;

Import["D:\\Projects\\sage\\unicyc_20_sgnlap_charpoly.json","JSON"];
graphList=Map[ImportString[#,"Graph6"]&]/@%;
{Length[graphList],Total@(Length/@graphList)}

matList=ParallelMap[FindDegSimMat,graphList];

matList=Flatten[matList,1]

{Length[matList],Total@(Length/@matList)}

Reap[Table[If[matrixRowSumQ[matList[[k]]],Sow[k],Nothing],{k,1,Length[matList]}]]