`has_eulerian_path()`

and `has_eulerian_cycle()`

checks whether there
is an Eulerian path or cycle in the input graph. `eulerian_path()`

and
`eulerian_cycle()`

return such a path or cycle if it exists, and throws
an error otherwise.

## Value

For `has_eulerian_path()`

and `has_eulerian_cycle()`

, a logical
value that indicates whether the graph contains an Eulerian path or cycle.
For `eulerian_path()`

and `eulerian_cycle()`

, a named list with two
entries:

- epath
A vector containing the edge ids along the Eulerian path or cycle.

- vpath
A vector containing the vertex ids along the Eulerian path or cycle.

## Details

`has_eulerian_path()`

decides whether the input graph has an Eulerian
*path*, i.e. a path that passes through every edge of the graph exactly
once, and returns a logical value as a result. `eulerian_path()`

returns
a possible Eulerian path, described with its edge and vertex sequence, or
throws an error if no such path exists.

`has_eulerian_cycle()`

decides whether the input graph has an Eulerian
*cycle*, i.e. a path that passes through every edge of the graph exactly
once and that returns to its starting point, and returns a logical value as
a result. `eulerian_cycle()`

returns a possible Eulerian cycle, described
with its edge and vertex sequence, or throws an error if no such cycle exists.

## See also

Graph cycles
`feedback_arc_set()`

,
`girth()`

,
`is_dag()`

Graph cycles
`feedback_arc_set()`

,
`girth()`

,
`is_dag()`

Graph cycles
`feedback_arc_set()`

,
`girth()`

,
`is_dag()`

Graph cycles
`feedback_arc_set()`

,
`girth()`

,
`is_dag()`

## Examples

```
g <- make_graph(~ A - B - C - D - E - A - F - D - B - F - E)
has_eulerian_path(g)
#> [1] TRUE
eulerian_path(g)
#> $epath
#> + 10/10 edges from 32d7a74 (vertex names):
#> [1] A--B B--C C--D B--D B--F A--F A--E D--E D--F E--F
#>
#> $vpath
#> + 11/6 vertices, named, from 32d7a74:
#> [1] A B C D B F A E D F E
#>
has_eulerian_cycle(g)
#> [1] FALSE
try(eulerian_cycle(g))
#> Error in eulerian_cycle(g) :
#> At core/paths/eulerian.c:613 : The graph does not have an Eulerian cycle. Invalid value
```