  Random links between otherwise distant nodes can greatly facilitate the
propagation of disease or information, provided contagion can be transmitted by
a single active node. However we show that when the propagation requires
simultaneous exposure to multiple sources of activation, called multiplex
propagation, the effect of random links is just the opposite: it makes the
propagation more difficult to achieve. We calculate analytical and numerically
critical points for a threshold model in several classes of complex networks,
including an empirical social network.
