IsConnectedGraph

Whether a Graph is connected — a single component; strongly connected when it has directed edges.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageConnectedGraphQ✓↗

IsConnectedGraph(g)true iff the graph is one component, respecting edge direction (false for a graph with no vertices).

Typed signatures

Type	Package	Applies
(value) -> boolean	combinatorics	always

Domain: Collections

Details

• Wolfram calls this ConnectedGraphQ; this library uses the Is… spelling everywhere.
• Respects direction, as Wolfram's ConnectedGraphQ does: a directed graph is connected only when it is strongly connected, so a single directed edge is not. IsTreeGraph still reads the underlying undirected graph.

Examples

Basic #

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In$\mathrm{IsConnectedGraph}(\mathrm{PetersenGraph}())$Out$\mathrm{True}$

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In$\mathrm{IsConnectedGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(3, 4)\bigr\rbrack))$Out$\mathrm{False}$

1 reaches 3 but 3 cannot get back: one weak piece, not strongly connected

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In$\mathrm{IsConnectedGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack\mathrm{DirectedEdge}(1, 2), \mathrm{DirectedEdge}(2, 1), \mathrm{DirectedEdge}(2, 3)\bigr\rbrack))$Out$\mathrm{False}$

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In$\mathrm{IsConnectedGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack\mathrm{DirectedEdge}(1, 2), \mathrm{DirectedEdge}(2, 3), \mathrm{DirectedEdge}(3, 1)\bigr\rbrack))$Out$\mathrm{True}$

About

Examples	4
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language

See also: ConnectedComponents, IsTreeGraph