A path is another
name for a route around a network or in space.

In graph theory,
a path in a graph is a sequence of vertices such that from each
of its vertices there is an edge to the next vertex in the sequence.
The first vertex is called the start vertex and the last vertex
is called the end vertex. Both of them are called end or terminal
vertices of the path. The other vertices in the path are internal
vertices.

A cycle is a path such that the start vertex and end vertex
are the same. Notice however that unlike with paths, any vertex
of a cycle can be chosen as the start, so the start is often not
specified.