A path is a sequence of nodes and links taken while navigating the network. This corresponds to Vannevar Bush's concept of a "trail," which he developed by analogy with the human brain.
The human mind [...] operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts, in accordance with some intricate web of trails carried by the cells of the brain. ("As We May Think" 101)
In early essays, Bush saw these trails as being immutable. Later, "memex [notices] which items in a trail are seldom used and which digressions are commonplace, and automatically [adjusts] the course of trail accordingly" (Oren 320). Compare this to the fading of footprints.
In a hypertext fiction, we might refer to a path as a storyline.