In an undirected graph [Undirected graph] \(G\), two vertices \(u\) and \(v\) are called connected if \(G\) contains a path [Path (graph theory)] from \(u\) to \(v\). Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length 1, i.e. by a single edge, the vertices are called adjacent.

## Connected graph

A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices.

## Disconnected graph

An undirected graph that is not connected is called disconnected.

## Weakly connected graph

A directed graph [Directed graph] is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph [Connected graph].

## Unilaterally connected graph

[A Directed graph] is unilaterally connected or unilateral (also called semiconnected) if it contains a directed path from u to v or a directed path from v to u for every pair of vertices u, v.

## Strongly connected graph

[A Directed graph] is strongly connected, or simply strong, if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u, v.

## Bibliography

*Wikipedia*, November. https://en.wikipedia.org/w/index.php?title=Connectivity_(graph_theory)&oldid=1120776993#Connected_vertices_and_graphs.