In graph theory and its practical networking applications, e.g., telecommunications and transportation, the problem of finding paths has particular importance. Selecting paths requires giving scores to the alternative solutions to drive a choice. While previous studies have provided comprehensive evaluation of single-path solutions, the same level of detail is lacking when considering sets of paths. This paper emphasizes that the path characterization strongly depends on the properties under consideration. While property-based characterization is also valid for single paths, it becomes crucial to analyse multiple path sets. From the above consideration, this paper proposes a mathematical approach, defining a functional model that lends itself well to characterizing the path set in its general formulation. The paper shows how the functional model contextualizes specific attributes.