  The microscopic and macroscopic dynamics of random networks is investigated
in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic
maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show
that a finite connectivity (of the order of a few tens) is able to sustain a
nontrivial collective dynamics even in the thermodynamic limit. Although the
network structure implies a non-additive dynamics, the microscopic evolution is
extensive (i.e. the number of active degrees of freedom is proportional to the
number of network elements).
