n. 1. (Graph theory) also called Hamiltonian walk. a walk in which each vertex, except possibly the first, occurs only once; it is a closed path (or cycle) if its endpoint is identical with its initial point. Compare trail.
2. (in a tree) a monotone sequence of edges, of which the first member is the root of the tree. 3. (Topology) the mapping inducing an arc; a path is a continuous mapping from the closed interval [0, 1] such that the images of the endpoints are the two given points. For example, x=cosπt and y = sinπt define a path onto the part of the unit circle in the upper half plane. See also path-connected.