SetDirectory@"C:\\drorbn\\AcademicPensieve\\Projects\\OU";
<< "OU-Programs.m"

β=VPB[5,{{-1,3,2},{-1,4,2},{-1,5,2},{-1,2,5},{-1,5,2},{-1,4,3},{-1,4,1},{-1,1,4},{-1,3,4},{1,4,5},{-1,2,4},{-1,2,5},{1,3,2},{1,1,2},{1,2,1},{1,2,3},{1,5,4},{1,4,5},{1,5,4},{1,2,4},{1,3,4},{-1,5,2},{-1,2,5},{-1,5,2},{-1,2,5},{-1,5,2},{-1,4,1},{-1,3,1},{-1,1,3},{-1,1,4},{-1,4,1},{-1,3,1},{1,4,3},{1,3,4},{-1,1,3},{-1,5,3},{1,3,2},{-1,3,2},{-1,3,5},{-1,3,1},{-1,3,4},{-1,4,3},{-1,1,3},{-1,5,3},{-1,2,3},{-1,3,2},{1,5,3},{1,1,3},{-1,3,4},{-1,4,3},{1,3,1},{1,4,1},{1,1,4},{1,1,3},{1,3,1},{1,4,1},{1,5,2},{1,2,5},{1,5,2},{1,2,5},{1,5,2},{-1,3,4},{-1,2,4},{-1,5,4},{-1,4,5},{-1,5,4},{-1,2,3},{-1,2,1},{-1,1,2},{-1,3,2},{1,2,5},{1,2,4},{-1,4,5},{1,3,4},{1,1,4},{1,4,1},{1,4,3},{1,5,2},{1,2,5},{1,5,2},{1,4,2},{1,3,2},{-1,5,4},{-1,4,5},{-1,5,4},{-1,4,5},{-1,5,4},{-1,2,1},{-1,3,1},{-1,1,3},{-1,1,2},{-1,2,1},{-1,3,1},{1,2,3},{1,3,2},{-1,1,3},{-1,5,3},{1,3,4},{1,4,3},{1,5,3},{1,1,3},{1,2,3},{1,3,2},{1,3,1},{1,3,5},{1,3,4},{-1,3,4},{1,5,3},{1,1,3},{-1,3,2},{-1,2,3},{1,3,1},{1,2,1},{1,1,2},{1,1,3},{1,3,1},{1,2,1},{1,5,4},{1,4,5},{1,5,4},{1,4,5},{1,5,4}}] /.{{1,i_,j_}:>(Subscript[σ, i,j]),{-1,i_,j_}:>(Subscript[(OverBar[σ]), i,j])}

Length@β-1

tab=Table[
Echo@{k-1, Take[β,k]};
Echo@ExtractionGraph[Take[β,k]],
{k,2,Length[β]}
];