Communication networks of the future will have to be secure against the potential threat of quantum attacks on extant encryption protocols. A possible solution being actively pursued theoretically and experimentally is that of constructing quantum networks (QN) which provide entanglement between network nodes as a resource for secure communications. Regions of the network where this resource can be readily accessed can implement quantum-safe protocols such as quantum key distribution (QKD). Whereas, regions of entanglement-scarcity will be restricted to quantum- resistant classical post-quantum cryptography (PQC) protocols. This division into distinct regions from the communication security viewpoint is what we refer to as the “security structure of QNs”. In this work, we will study the security-structure of QNs via the concomitant entanglement-structure of QNs based on practically realisable distributions of network edge-entanglement parameters. We will determine the parametric size of the expected quantum-safe region where QKD can be efficiently implemented; simultaneously, the size of the quantum-resistant regions where very little entanglement can be accessed thereby making QKD infeasible and PQC necessary for communication security in the quantum era