# Connected Graph **A [[graph]] in which every pair of vertices is connected by a [[path]].** ![[ConnectedDisconnectedGraph.svg|600]] > [!NOTE] Connected Graph > A *connected graph* is a graph in which between every pair of vertices there *exists a path*. > > A graph that is not connected is referred to as a *disconnected graph*. An edge whose removal from a graph makes it disconnected is known as a *bridge*. ## Directed graphs There are several definitions of connectivity related to [[Graph#Directed graph|directed graphs]]: - *weakly connected* - the graph formed from replacing all of its directed edges with undirected edges is connected. - *unilaterally connected* - for all pairs of vertices $v, w$, either a directed path from $v$ to $w$ or a directed path from $w$ to $v$ exists but not necessarily both. - *[[Strongly Connected Component|strongly connected]]* - for all pairs of vertices $v, w$, a directed path from $v$ to $w$ and from $w$ to $v$ exists.