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Path

In mathematics (graph theory)

A path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct.

Since the vertices are distinct, so are the edges.

Terms

Walk, trail and path

  • Walk: A finite or infinite sequence of edges which joins a sequence of vertices
  • Trail: A walk in which all edges are distinct
  • Path: A trail in which all vertices (and hence all edges too) are distinct

Directed walk, directed trail, directed path

  • Directed walk: A finite or infinite sequence of edges directed in the same direction which joins a sequence of vertices
  • Directed trail: A directed walk in which all edges are distinct
  • Directed path: A directed trail in which all vertices (and hence all edges too) are distinct

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