  We report numerical evidence that an epidemic-like model, which can be
interpreted as the propagation of a rumor, exhibits critical behavior at a
finite randomness of the underlying small-world network. The transition occurs
between a regime where the rumor "dies" in a small neighborhood of its origin,
and a regime where it spreads over a finite fraction of the whole population.
Critical exponents are evaluated, and the dependence of the critical randomness
with the network connectivity is studied. The behavior of this system as a
function of the small-network randomness bears noticeable similarities with an
epidemiological model reported recently [M. Kuperman and G. Abramson, Phys.
Rev. Lett. 86, 2909 (2001)], in spite of substantial differences in the
respective dynamical rules.
