Editing Path (graph theory) (section)

== Examples ==
* A graph is [[Connectivity (graph theory)|connected]] if there are paths containing each pair of vertices.
* A directed graph is [[Strongly-connected digraph|strongly connected]] if there are oppositely oriented directed paths containing each pair of vertices.
* A path such that no graph edges connect two nonconsecutive path vertices is called an [[induced path]].
* A path that includes every vertex of the graph without repeats is known as a [[Hamiltonian path]].
* Two paths are ''vertex-independent'' (alternatively, ''internally disjoint'' or ''internally vertex-disjoint'') if they do not have any internal vertex or edge in common. Similarly, two paths are ''edge-independent'' (or ''edge-disjoint'') if they do not have any edge in common.  Two internally disjoint paths are edge-disjoint, but the converse is not necessarily true.
* The [[Distance (graph theory)|distance]] between two vertices in a graph is the length of a shortest path between them, if one exists, and otherwise the distance is infinity.
* The diameter of a connected graph is the largest distance (defined above) between pairs of vertices of the graph.