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* A graph is [[Connectivity (graph theory)|connected]] if there are paths containing each pair of vertices.

* 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 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 such that no graph edges connect two nonconsecutive path vertices is called an [[induced path]].

没有图的边连接两个不连续的路径顶点的路径称为'''<font color="#ff8000">诱导路径 Induced Path</font>'''。

没有边连接两个不连续的路径顶点的路径称为'''<font color="#ff8000">诱导路径 Induced Path</font>'''。

* A path that includes every vertex of the graph is known as a [[Hamiltonian path]].

* A path that includes every vertex of the graph is known as a [[Hamiltonian path]].

* Two paths are ''vertex-independent'' (alternatively, ''internally vertex-disjoint'') if they do not have any internal vertex in common. Similarly, two paths are ''edge-independent'' (or ''edge-disjoint'') if they do not have any internal edge in common.  Two internally vertex-disjoint paths are edge-disjoint, but the converse is not necessarily true.

* Two paths are ''vertex-independent'' (alternatively, ''internally vertex-disjoint'') if they do not have any internal vertex in common. Similarly, two paths are ''edge-independent'' (or ''edge-disjoint'') if they do not have any internal edge in common.  Two internally vertex-disjoint paths are edge-disjoint, but the converse is not necessarily true.

如果两条路径没有任何共同的内部顶点，则它们与顶点无关(或者，内部顶点不相交)。类似地，如果两条路径没有任何共同的内边，则它们是边独立的(或边不相交)。两条内部顶点不相交的路径是边不相交的，但反过来也不一定是正确的。

如果两条路径没有任何共同的内部顶点，那么它们与顶点无关(换言之，内部顶点不相交)。类似地，如果两条路径没有任何共同的内边，那么它们是边独立的(或边不相交)。两条内部顶点不相交的路径的边也不相交，但反之未必正确的。

* 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 [[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.

* The diameter of a connected graph is the largest distance (defined above) between pairs of vertices of the graph.

连接图的直径是图的顶点对之间的最大距离（如上定义）。

连接图的直径是图的顶点对之间的最大距离（如上定义）。

== Finding paths 路径寻找==

== Finding paths 路径寻找==