Editing Graph (discrete mathematics) (section)

=== Connected graph ===
{{main|Connectivity (graph theory)}}
In an undirected graph, an unordered pair of vertices {{nowrap|{{mset|''x'', ''y''}}}} is called ''connected'' if a path leads from ''x'' to ''y''. Otherwise, the unordered pair is called ''disconnected''.

A ''connected graph'' is an undirected graph in which every unordered pair of vertices in the graph is connected. Otherwise, it is called a ''disconnected graph''.

In a directed graph, an ordered pair of vertices {{nowrap|(''x'', ''y'')}} is called ''strongly connected'' if a directed path leads from ''x'' to ''y''. Otherwise, the ordered pair is called ''weakly connected'' if an undirected path leads from ''x'' to ''y'' after replacing all of its directed edges with undirected edges. Otherwise, the ordered pair is called ''disconnected''.

A ''strongly connected graph'' is a directed graph in which every ordered pair of vertices in the graph is strongly connected. Otherwise, it is called a ''weakly connected graph'' if every ordered pair of vertices in the graph is weakly connected. Otherwise it is called a ''disconnected graph''.

A ''[[k-vertex-connected graph]]'' or ''[[k-edge-connected graph]]'' is a graph in which no set of {{nowrap|''k'' − 1}} vertices (respectively, edges) exists that, when removed, disconnects the graph. A ''k''-vertex-connected graph is often called simply a ''k-connected graph''.