# ConnectedGraphQ

yields True if the graph g is connected, and False otherwise.

# Details • ConnectedGraphQ works for any graph object.
• A graph is connected if there is a path between every pair of vertices.

# Examples

open allclose all

## Basic Examples(2)

Test whether a graph is connected:

A graph with isolated vertices is not connected:

## Scope(6)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

ConnectedGraphQ gives False for anything that is not a connected graph:

ConnectedGraphQ works with large graphs:

## Applications(1)

Compute the probability that the WattsStrogatz random graph model is connected:

## Properties & Relations(5)

The graph distance matrix of a connected graph does not have entries:

Connected graph:

Disconnected graph:

The minimum number of edges in a connected graph with vertices is :

A path graph with vertices has exactly edges:

A connected graph has vertex degree greater than for the underlying simple graph:

A disconnected graph:

An undirected tree is connected:

An undirected path is connected:

Introduced in 2010
(8.0)