  The connectivity of individual neurons of large neural networks determine
both the steady state activity of the network and its answer to external
stimulus. Highly diluted random networks have zero activity. We show that
increasing the network connectivity the activity changes discontinuously from
zero to a finite value as a critical value in the connectivity is reached.
Theoretical arguments and extensive numerical simulations indicate that the
origin of this discontinuity in the activity of random networks is a first
order phase transition from an inactive to an active state as the connectivity
of the network is increased.
