Can anyone help me understand why the following happens?

N := GraphTheory[Digraph]({[1,3],[3,9],[9,27]});

GraphTheory[IsNetwork](N);

and

M := GraphTheory[Digraph]({[1,2],[2,4],[4,8]});

GraphTheory[IsNetwork](M);

both indicate that the graph is not a network. On the other hand, for numbers n other than 2 and 3, Maple does recognize the graph {[1,n],[n,n^2],[n^2,n^3]} as a network.

This procedure that I wrote:

FindNetwork := proc()

local G, N, b, i, m;

for b from 2 to 100 do

for m from 1 to 10 do

G := {};

for i from 0 to m do

G := G union {[b^i,b^(i+1)]};

end do;

N := GraphTheory[Digraph](G);

if not GraphTheory[IsNetwork](N,1,b^(m+1)) then

printf("failed: %d^%d\n", b, m);

end if;

end do;

end do;

end proc:

indicates that for b=2 and b=3, and any value of m, the graph is not a network, but it is for all other values of b and m, it is.

Can anyone please explain why?

Thanks.