I'm not sure if they mean networked = computer -- if not I've read a whole bunch of stories where there are missionaries of hope and outposts of civilisation bootstapping civilisation... I seem to remember a couple by Andre Norton, even.

A surviving network of computers operational over hundreds of miles or across continents would be a bit daft. And technology likewise often requires a deal of co-operative production -- way more than a hand-to-mouth society can rustle up. But then I think it was 'Threads' -- post-nuclear attack drama -- that showed people fighting over a plastic wrapped loaf of bread some months after the 'end' o.o