Abstract This paper presents a model for path-based growing network with preferential attachment motivated by the deployment of quantum key distribution networks. The model is based on a network constructed from path segments of n nodes on average to mimic real-world quantum key distribution network architectures. Using continuum formalism and the rate equation method, we derive degree exponent, exact degree distributions and demonstrate properties similar to random networks. The theoretical framework incorporates preferential attachment with variable crossover rates and strategic shortcuts, the satellite links. The approach is validated through extensive simulations implemented in Python. Key findings reveal that network robustness, measured by critical fraction for giant component loss, increases with crossover rate and number of satellite links but decreases with segment length. Average distance scales logarithmically with network size, directly impacting secret key consumption during relaying processes in quantum key distribution networks. While preferential attachment enhances connectivity, the model network does not achieve ultra-small world properties of scale-free networks that would minimize key consumption, providing insights for designing cost-effective quantum communication infrastructures.
Weiss et al. (Sun,) studied this question.