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_acyclic(),
is_dag()
Related documentation in the C library
igraph_is_eulerian(), igraph_eulerian_path(), igraph_eulerian_cycle().
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 67f3057 (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 67f3057:
#> [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 vendor/cigraph/src/paths/eulerian.c:615 : The graph does not have an Eulerian cycle. Input problem has no solution