Today you need to become an expert in TCP / IP protocols. Everything from ARP, DNS, UDP, ICMG, BGP and so on. Most networks are IP based, with IP based firewalls. Firewalls will allow, for example, "TCP traffic on port 80". You should be able to understand if this traffic is really web surfing, a DOS attack or other evil. This can only be achieved with a detailed understanding of how IP networks work. The same goes for other protocols such as DNS. In addition, a deeper understanding of network communications and other vehicles (such as cell phone networks or Wi-Fi networks) will be important. I believe that it depends on what you mean by "network security" - for me it is below the application level.
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