  In the past few years, several studies have explored the topology of
interactions in different complex systems. Areas of investigation span from
biology to engineering, physics and the social sciences. Although having
different microscopic dynamics, the results demonstrate that most systems under
consideration tend to self-organize into structures that share common features.
In particular, the networks of interaction are characterized by a power law
distribution, $P(k)\sim k^{-\alpha}$, in the number of connections per node,
$k$, over several orders of magnitude. Networks that fulfill this propriety of
scale-invariance are referred to as ``scale-free''. In the present work we
explore the implication of scale-free topologies in the antiferromagnetic (AF)
Ising model and in a stochastic model of opinion formation. In the first case
we show that the implicit disorder and frustration lead to a spin-glass phase
transition not observed for the AF Ising model on standard lattices. We further
illustrate that the opinion formation model produces a coherent, turbulent-like
dynamics for a certain range of parameters. The influence, of random or
targeted exclusion of nodes is studied.
