yields True if the graph g is connected, and False otherwise.
- ConnectedGraphQ works for any graph object.
- A graph is connected if there is a path between every pair of vertices.
Examplesopen allclose all
Basic Examples (2)
ConnectedGraphQ gives False for anything that is not a connected graph:
ConnectedGraphQ works with large graphs:
Properties & Relations (5)
The graph distance matrix of a connected graph does not have entries:
The minimum number of edges in a connected graph with vertices is :
A path graph with vertices has exactly edges:
The sum of the vertex degrees of a connected graph is greater than for the underlying simple graph:
An undirected tree is connected:
Wolfram Research (2010), ConnectedGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/ConnectedGraphQ.html.
Wolfram Language. 2010. "ConnectedGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ConnectedGraphQ.html.
Wolfram Language. (2010). ConnectedGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ConnectedGraphQ.html