  The rate and security of quantum communications between users placed at
arbitrary points of a quantum communication network depend on the structure of
the network, on its extension and on the nature of the communication channels.
In this work we propose a strategy for the optimization of trusted-relays based
networks that intertwines classical network approaches and quantum information
theory. Specifically, by suitably defining a quantum communication efficiency
functional, we identify the optimal quantum communication connections through
the network by balancing security and the quantum communication rate. The
optimized network is then constructed as the network of the maximal quantum
communication efficiency connections and its performance is evaluated by
studying the scaling of average properties as functions of the number of nodes
and of the network spatial extension.
