  On directed Barabasi-Albert networks with two and seven neighbours selected
by each added site, the Ising model with spin S=1/2 was seen not to show a
spontaneous magnetisation. Instead, the decay time for flipping of the
magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms,
but for Wolff cluster flipping the magnetisation decayed exponentially with
time. However, on these networks the Ising model spin S=1 was seen to show a
spontaneous magnetisation.
  In this model with spin S=1 a first-order phase transition for values of
connectivity z=2 and z=7 is well defined. On these same networks the Potts
model with q=3 and 8 states is now studied through Monte Carlo simulations.
  We have obtained also for q=3 and 8 states a first-order phase transition for
values of connectivity z=2 and z=7 of the directed Barabasi-Albert network.
Theses results are different from the results obtained for same model on
two-dimensional lattices, where for q=3 the phase transition is of second
order, while for q=8 the phase transition is first-order.
