with(networks):

DegG:=proc(_G) local _i,_D,_N,_M;
   _M:=adjacency(_G);
   _N:=LinearAlgebra[RowDimension](convert(_M,Matrix)):
   _D:=Matrix(_N,_N,0);
   for _i from 1 to _N  do
      _D[_i,_i]:=add(_M[_i,_j],_j=1.._N);
   od:
   return _D;
end proc:

LapG:=proc(_G)
    return adjacency(_G)-DegG(_G);
end proc:

SNF:=proc(_G) local _N,_SF;
    _N:=LinearAlgebra[RowDimension](convert(adjacency(_G),Matrix)):
    _SF:=linalg[ismith](LapG(_G));
    return [seq(_SF[_i,_i],_i=1.._N)];
end proc:

fSNF:=proc(_G)
    return ifactor(SNF(_G));
end proc:

oSNF:=proc(_G) local ords,i,j,_list,_n;
   _list:=SNF(_G);
   _n:=LinearAlgebra[RowDimension](convert(adjacency(_G),Matrix)): 
   j:=1:
   for i from 1 to _n do
   #print(_list,_list[i]); 
      if (_list[i] <> 0 and _list[i]<> 1) then
         ords[j]:=_list[i]:
         j:=j+1:
      fi:
    od:
    if j=1 then ords[1]:=0: fi;
    return convert(ords,list);
end proc:

ofSNF:=proc(_G)
    return ifactor(oSNF(_G));
end proc:



LabelIt:=proc(_G,_labels) local _n;
    _n:=LinearAlgebra[RowDimension](convert(adjacency(_G),Matrix));
    return graph(_labels,subs({seq(i=_labels[i],i=1.._n)},ends(_G)));
end proc:

UnLabel:=proc(_G) local _n;
    _n:=LinearAlgebra[RowDimension](convert(adjacency(_G),Matrix));
     return graph({seq(i,i=1.._n)},subs({seq(v[i]=i,i=1.._n)},ends(_G)));
end proc:

gdunion:=proc(_list) local _i,_nextLab,_LGraphs,_numGs,_numVs,_totVs,_ansa;
   _numGs:=LinearAlgebra[ColumnDimension](convert(_list,Matrix));
   _totVs:=0:
   for _i from 1 to _numGs do
      _numVs[_i]:=LinearAlgebra[RowDimension](convert(adjacency(_list[_i]),Matrix)):
      _LGraphs[_i]:=LabelIt(_list[_i],[seq(v[j],j=_totVs+1.._totVs+_numVs[_i])]);
      _totVs:=_totVs+_numVs[_i];
   od:

   _ansa:=_LGraphs[1];
   for _i from 2 to _numGs do
      _ansa:=gunion(_ansa,_LGraphs[_i]);
   od;
   return( UnLabel(_ansa));
end proc:

NPath:=proc(_N)
   return delete({_N+2},cycle(_N+2));
end proc:

KRho:=proc(_n,_subbie) local biggie;
if( _n >= LinearAlgebra[RowDimension](incidence(_subbie)) ) then
   biggie:=complete(_n):
   return complement(graph({seq(i,i=1.._n)},ends(_subbie)),biggie);
else
   print(cat("Must take complement in larger complete graph. Received K_", _n,", but subgraph has ", LinearAlgebra[RowDimension](incidence(_subbie)), " vertices!"));
   return graph({1},[1,1]):
fi: 
end proc:

ModPath:=proc(_A,_M, _N) local i, paf,first,last;
   paf:={}:
   first:=-1:
   for i from 1 to _N-_M do
       if (i mod _M = _A mod _M ) then
           if ( first = -1 ) then
              first:=i;
           fi;
       paf:=paf union {{i,i+_M}};
       last:=i+_M;
       fi;
   od:
   if( first mod _M = last mod _M ) then
       paf:=paf union {{first,last}}
   fi;
   return graph({seq(j,j=1.._N)},paf);
end proc:

ParPath:=proc(_N)
    return gunion(ModPath(1,2,_N),ModPath(2,2,_N));
end proc:

SkipN:=proc(_M,_N) local paf, i, j, ModN;
    ModN:=x->piecewise((x-_N*trunc(x/_N))<>0,x-_N*trunc(x/_N) mod _N,_N):
    paf:={};
    for i from 1 to _N do   
       paf:=paf union {{i ,ModN(i+_M)},{i ,ModN(i-_M)}}; 
    od;
    return graph({seq(i,i=1.._N)},paf);
end proc:

DisPaths:=proc(_list) return DisjointPaths(_list); end proc:

DisjointPaths:=proc(_list) local _numGs;
    _numGs:=LinearAlgebra[ColumnDimension](convert(_list,Matrix));
    return gdunion([seq(NPath(_list[i]),i=1.._numGs)]);
end proc:

LineGraph:=proc(_G) local i,Vset, Eset;
  Eset:={}:
  Vset:=ends(_G):
  for i from 1 to LinearAlgebra[RowDimension](incidence(_G)) do  
    Eset:=Eset union combinat[choose](ends(incident(i,_G),_G),2);
  od;

  return graph(Vset,Eset);
end proc:


print("Added Commands: LapG, DegG, SNF, fSNF, oSNF, ofSNF, gdunion, NPath, ModPath, ParPath, DisPaths, SkipN, KRho, LineGraph");