Help:=proc(): print(`G(n), Friends(G,v), FriendsS(G,Sv)  `): 
print(`Cc(G,v) , IsConnected(G,n), CG(n)`):
end:

with(combinat):

#G(n): the set of ALL labelled graphs on n vertices
G:=proc(n): powerset(convert(choose(n,2),set)) : end:

#Friends(G,v): all the friends of vertex v in G
Friends:=proc(G,v) local F,e:
F:={}:

for e in G do
 if member(v,e) then

   F:=F union {{op(e)} minus {v} }[1]:
 fi:
od:

F union {v}:

end:


#The collective set of friends of Sv in G
FriendsS:=proc(G,Sv) local v:

{seq( op(Friends(G,v)), v in Sv)}:
end:

#IsConnected(G,n): Is the graph G (on {1, ..., n}) connected
IsConnected:=proc(G,n) local i:

evalb({seq(i,i=1..n)}=Cc(G,1)):
end:




#Cc(G,v): the transitive closure of friendships of v in G
Cc:=proc(G,v) local S,NewS:


S:={v}:


NewS:=FriendsS(G,S):

while NewS<>S do
  S:=NewS:
  NewS:=FriendsS(G,NewS):
od:
NewS:
end:


CG:=proc(n) local S,C,s:
S:=G(n):
C:={}:

 for s in S do
   if IsConnected(s,n) then
     C:={op(C),s}:
   fi:
 od:
C:
end: