Network connectivity is a fundamental property affecting network performance. Given the reliability of each link, network connectivity determines the probability that a message can be delivered from the source to the destination. In this thesis, we study the directed network connectivity where the message will be forwarded toward the destination hop by hop, so long as the neighbor(s) is (are) closer to the destination. Directed connectivity, closely related to directed percolation, is very complicated to calculate. The existing state-of-the-art can only calculate directed connectivity for a lattice network up-to-the size of 10 × 10. In this thesis, we devise a new approach that is simpler and more scalable and can handle general network topology and heterogeneous links. The proposed approach uses an unambiguous hop count to divide the networks into hops and gives two steps of pre-process to transform hop-count ambiguous networks into unambiguous ones, and derive the end-to-end connectivity. Then, using the Markov property to obtain the state transition probability hop by hop. Second, with tens of thousands of Low Earth Orbit (LEO) satellites covering the Earth, LEO satellite networks can provide coverage and services that are otherwise not possible using terrestrial communication systems. The regular and dense LEO satellite constellation also provides new opportunities and challenges for network protocol design. In this thesis, we apply the directed connectivity analytical model on LEO satellite backbone networks to ensure ultra-reliable and low-latency (URLL) services using LEO networks, and propose a directed percolation routing (DPR) algorithm to lower the cost of transmission without sacrificing speed. Using Starlink constellation (with 1,584 satellites) as an example, the proposed DPR can achieve a few to tens of milliseconds latency reduction for inter-continental transmissions compared to the Internet backbone, while maintaining high reliability without link-layer retransmissions. Finally, considering the link redundancy overhead and delay/reliability tradeoff, DPR can control the size of percolation. In other words, we can choose a part of links to be active links considering the reliability and cost tradeoff. / Graduate