has_eulerian_path: Find Eulerian paths or cycles in a graph

In igraph: Network Analysis and Visualization

Find Eulerian paths or cycles in a graph

Description

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.

Usage

has_eulerian_path(graph)

has_eulerian_cycle(graph)

eulerian_path(graph)

eulerian_cycle(graph)

Arguments

graph

An igraph graph object

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.

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.

Related documentation in the C library

igraph_is_eulerian(), igraph_eulerian_path(), igraph_eulerian_cycle().

See Also

Graph cycles feedback_arc_set(), girth(), is_acyclic(), is_dag()

Examples

g <- make_graph(~ A - B - C - D - E - A - F - D - B - F - E)

has_eulerian_path(g)
eulerian_path(g)

has_eulerian_cycle(g)
try(eulerian_cycle(g))

igraph documentation built on Oct. 20, 2024, 1:06 a.m.