Abstract: Systems and methods for network service path analysis analyze and manage the delivery of applications over a network. A program running on a computer utilizes a Layer 3 topology of a computer network to create a directed graph representing deliverability of packets across the network. By analyzing access control lists and firewall rule sets from the network, along with modeling routing protocol behavior and policy as packet filters, the program performs a series of matrix multiplications, using an optimized decomposition of the IP packet space. The resulting matrix contains all of the path information for all deliverable packets. The matrix populates a network path database that captures the set of packets deliverable between any pair of Internet Protocol addresses in the network.