  As an extension of quantum key distribution, secure communication among
multiple users is an essential task in a quantum network. When the quantum
network structure becomes complicated with a large number of users, it is
important to investigate network issues, including security, key management,
latency, reliability, scalability, and cost. In this work, we utilize the
classical and graph theories to address two critical issues in a quantum
network: security and key management. First, we design a communication scheme
with the highest security level that trusts a minimum number of intermediate
nodes. Second, when the quantum key is a limited resource, we design key
management and data scheduling schemes to optimize the utility of data
transmission. Our results can be directly applied to the current metropolitan
and free-space quantum network implementations and potentially be a standard
approach for future quantum network designs.
