What the...?
Network Admin low stress? Which version of the term are you using, Server/System Admin, or Router Admin?
I've been a Network (System) Admin - it means you are the one person who's responsibility is the upkeep of the entire server network that keeps the company up and running. Basically, if there's any blip or bump in service, you are responsible for it.
This would include, of course, after hours and mandate weekend upgrades, troubleshooting, etc.
If you are a Network (Router) Admin, than your responsibility is every hub, switch, router, cable, server closet, in the company, and again if there is any loss or degradation in service you are on the hook for it. Every upgrade or main job is done after hours, since you can't take the network down in any company that would have a Network Admin position.
Also - both of those positions (unless there is someone higher up to take the job) are responsible for the entire computer security of the company.
Depending on the company, that part of the job alone can keep you up at nights.
Of course, I didn't get my AA in this - just 18 years of work experience in the field.