pathsthose

Pathsthose is a term encountered in discussions of graph theory and graph query languages to denote a class of constrained paths that connect a set of source nodes to a set of target nodes while satisfying a predicate. The name combines "paths" with "those" to signal that only designated destinations are relevant.

In formal terms, let G = (V,E) be a directed graph, with S ⊆ V as sources and T ⊆ V as targets, and let φ be a predicate that can reference edges, vertices, or path structure. A path p = (v0, v1, ..., vk) is a pathsthose if v0 ∈ S, vk ∈ T, and every consecutive pair (vi, vi+1) forms an edge in E, together with φ(p) holding. Variants may require paths to be simple (no repeated vertices), may constrain path length, or impose additional conditions on intermediate vertices or edges.

From a computational perspective, pathsthose can be expressed in query form as a combination of source and target specifications with a constrained path expression, such as a regular path constraint or a more expressive predicate. They are used to extract routes or connections that meet specific requirements, rather than merely listing all connections between two sets.

Applications of the concept include social-network analysis, where all chains of connections from a given user to a set of influential figures are examined under a length bound or label restrictions; and routing or planning contexts, where feasible paths from depots to destinations must satisfy policy, capacity, or safety constraints.

Pathsthose is not a standard term in formal graph theory but appears in theoretical discussions and teaching materials as a way to frame constrained reachability problems. It overlaps with constrained path queries and reachability with predicates, and it helps distinguish selective destination-focused path analysis from unconstrained path enumeration.