  With the growing complexity of quantum key distribution (QKD) network
structures, aforehand topology design is of great significance to support a
large-number of nodes over a large-spatial area. However, the exclusivity of
quantum channels, the limitation of key generation capabilities, the variety of
QKD protocols and the necessity of untrusted-relay selection, make the optimal
topology design a very complicated task. In this research, a hybrid QKD network
is studied for the first time from the perspective of topology, by analyzing
the topological differences of various QKD protocols. In addition, to make full
use of hybrid networking, an analytical model for optimal topology calculation
is proposed, to reach the goal of best secure communication service by
optimizing the deployment of various QKD devices and the selection of
untrusted-relays under a given cost limit. Plentiful simulation results show
that hybrid networking and untrusted-relay selection can bring great
performance advantages, and then the universality and effectiveness of the
proposed analytical model are verified.
