Due to the intrinsic point-to-point characteristic of quantum key distribution (QKD) systems, it is necessary to study and develop QKD network technology to provide a secure communication service for a large-scale of nodes over a large area. Considering the quality assurance required for such a network and the cost limitations, building an effective mathematical model of a QKD network becomes a critical task. In this paper, a flow-based mathematical model is proposed to describe a QKD network using mathematical concepts and language. In addition, an investigation on QKD network topology evaluation was conducted using a unique and novel QKD network performance indicator, the Information-Theoretic Secure communication bound, and the corresponding linear programming-based calculation algorithm. A large number of simulation results based on the topologies of SECOQC network and NSFNET network validate the effectiveness of the proposed model and indicator.