First Incarnation - 1985
Superman and Batman encounter the Network, a group of super-villains whose powers are patterned after TV effects, and who warp out a discotheque full of people into another dimension. Later, they send Batman there as well. Superman was able to rescue Batman and the duo were able to defeat the Network.
Second Incarnation -2002
The Network was a criminal organization that plotted revenge against the Rossetti mafia family for the death of their leader's lover. They also desired to steal from Wayne Enterprises and kill Batman and his team. A small group of them were given superpowers from the Monitor just before the Crisis on Infinite Earths .