Greetings.
I did a search here to no avail.
Does the “Network” Shield need to be running, if I am not on a “Network”? Or is my query here over-simplified?
Thanks in advance,
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Yes. The network shield protects the computer connected to Internet network 
It doesn’t have anything to do wit actually being on a network (I’m not either) and I would say it is an essential element of your security.
Did you check the avast Help file ?
See image extract of help file, it also provides protection against malicious web sites.
Good enough - thank you both very much!
No problem, glad I could help.
Welcome to the forums.