pathsthrough

Pathsthrough is a concept used in graph theory and information-flow analysis to refer to the set of all possible traversal paths through a network or system from designated starting points to designated endpoints. In a directed graph G=(V,E) with sources S⊆V and sinks T⊆V, a path p=(v0,...,vk) is in the pathsthrough if v0∈S, vk∈T, and (vi,vi+1)∈E for all i. The collection P of all such simple paths constitutes the pathsthrough. When the graph is a DAG, P can be computed or counted efficiently with dynamic programming; in general graphs the number of paths may grow exponentially, making exact enumeration intractable for large networks.

Pathsthrough is used to characterize how information, materials, or signals may propagate, and to support analyses of latency, reliability, and exposure. In software engineering, the concept relates to path coverage and testing strategies that aim to exercise all feasible routes from inputs to outputs. In network design and security, pathsthrough supports threat modeling by identifying potential attack paths, and in data systems it aids in provenance and data lineage studies by tracing possible data routes.

Common computational approaches include path enumeration for DAGs, counting paths via dynamic programming, Monte Carlo sampling for approximate estimates, and automata-based representations to express constraints on allowed paths. Related concepts include reachability, path coverage, and path diversity.