**Connection and components**

Two vertices are said to be *connected* when a path between them exists. A graph is said
to be *connected* when every two of its vertices are connected. A graph that is not
connected is *disconnected.*

A *connected component (* or simply *component*) of a graph is the maximal subgraph
whose vertices are all connected. A connected graph has a single component, and that is
the graph itself. A disconnected graph will have at least two components. A block is a special kind of connected graph or subgraph.

This graph is connected. | |

This graph is not connected. |

Sometimes there is no way of looking at a drawing such as the disconnected one without any other context and know if it is a single graph that is not connected or two graphs that are drawn near one another. The context must make it clear that it is one graph.

*Connectivity* is the term used to refer to the number of edges or vertices you
must delete form a graph in order to disconnect it.

Copyright © 1999-2000 SciMathMN