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.