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# connected(+Graph)

Guarantees that an undirected graph Graph is connected.
Graph
A graph.

## Description

Guarantees that an undirected graph Graph is connected, i.e., that each vertex is reachable from any other one.

### Fail Conditions

Fails if Graph is not an undirected graph variable or if Graph can not be constrained to be connected.

## Examples

```?- connected(G).
No.

?- V`::[1,2]..[1,2,3,4], E`::[]..[[1,3],[2,4],[3,1],[4,2]], undirgraph(G,V,E), connected(G).
No.

?- V`::[1,2]..[1,2,3], E`::[]..[[1,2],[1,3],[2,1],[2,3],[3,1],[3,2]], undirgraph(G,V,E), connected(G), graph_labeling(G).
V = [1, 2]
E = [[1, 2], [2, 1]]
G = undirgraph([1, 2], [[1, 2], [2, 1]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 3], [2, 3], [3, 1], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 3], [2, 3], [3, 1], [3, 2]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [2, 1], [2, 3], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 2], [2, 1], [2, 3], [3, 2]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [1, 3], [2, 1], [3, 1]]
G = undirgraph([1, 2, 3], [[1, 2], [1, 3], [2, 1], [3, 1]])
Yes ? ;

V = [1, 2, 3]
E = [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]
G = undirgraph([1, 2, 3], [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]])
Yes
```