Path (graph Theory)

Path (graph Theory)

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. A path may be infinite, but a finite path always has a first vertex, called its start vertex, and a last vertex, called its end vertex. Both of them are called 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. The choice of the start vertex in a cycle is arbitrary.

Paths and cycles are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). Korte et al. (1990) cover more advanced algorithmic topics concerning paths in graphs.

The vertices of a path are said to be connected. The vertices of a directed cycle are said to be strongly connected.