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.