Finds all simple cycles in a graph.

This function lists all simple cycles in a graph within a range of cycle lengths. A cycle is called simple if it has no repeated vertices.

Multi-edges and self-loops are taken into account. Note that typical graphs have exponentially many cycles and the presence of multi-edges exacerbates this combinatorial explosion.

simple_cycles(
  graph,
  mode = c("out", "in", "all", "total"),
  min = NULL,
  max = NULL
)

Arguments

graph

The input graph.

mode

Character constant specifying how to handle directed graphs. out follows edge directions, in follows edges in the reverse direction, and all ignores edge directions. Ignored in undirected graphs.

min

Lower limit on cycle lengths to consider. NULL means no limit.

max

Upper limit on cycle lengths to consider. NULL means no limit.

Value

A named list, with two entries:

vertices

The list of cycles in terms of their vertices.

edges

The list of cycles in terms of their edges.

See also

Graph cycles feedback_arc_set(), feedback_vertex_set(), find_cycle(), girth(), has_eulerian_path(), is_acyclic(), is_dag()

Related documentation in the C library

simple_cycles().

Examples

g <- graph_from_literal(A -+ B -+ C -+ A -+ D -+ E +- F -+ A, E -+ E, A -+ F, simplify = FALSE)
simple_cycles(g)
#> $vertices
#> $vertices[[1]]
#> + 3/6 vertices, named, from c4da9ad:
#> [1] A B C
#> 
#> $vertices[[2]]
#> + 2/6 vertices, named, from c4da9ad:
#> [1] A F
#> 
#> $vertices[[3]]
#> + 1/6 vertex, named, from c4da9ad:
#> [1] E
#> 
#> 
#> $edges
#> $edges[[1]]
#> + 3/9 edges from c4da9ad (vertex names):
#> [1] A->B B->C C->A
#> 
#> $edges[[2]]
#> + 2/9 edges from c4da9ad (vertex names):
#> [1] A->F F->A
#> 
#> $edges[[3]]
#> + 1/9 edge from c4da9ad (vertex names):
#> [1] E->E
#> 
#> 
simple_cycles(g, mode = "all") # ignore edge directions
#> $vertices
#> $vertices[[1]]
#> + 3/6 vertices, named, from c4da9ad:
#> [1] A B C
#> 
#> $vertices[[2]]
#> + 4/6 vertices, named, from c4da9ad:
#> [1] A D E F
#> 
#> $vertices[[3]]
#> + 4/6 vertices, named, from c4da9ad:
#> [1] A D E F
#> 
#> $vertices[[4]]
#> + 2/6 vertices, named, from c4da9ad:
#> [1] A F
#> 
#> $vertices[[5]]
#> + 1/6 vertex, named, from c4da9ad:
#> [1] E
#> 
#> 
#> $edges
#> $edges[[1]]
#> + 3/9 edges from c4da9ad (vertex names):
#> [1] A->B B->C C->A
#> 
#> $edges[[2]]
#> + 4/9 edges from c4da9ad (vertex names):
#> [1] A->D D->E F->E F->A
#> 
#> $edges[[3]]
#> + 4/9 edges from c4da9ad (vertex names):
#> [1] A->D D->E F->E A->F
#> 
#> $edges[[4]]
#> + 2/9 edges from c4da9ad (vertex names):
#> [1] F->A A->F
#> 
#> $edges[[5]]
#> + 1/9 edge from c4da9ad (vertex names):
#> [1] E->E
#> 
#> 
simple_cycles(g, mode = "all", min = 2, max = 3) # limit cycle lengths
#> $vertices
#> $vertices[[1]]
#> + 3/6 vertices, named, from c4da9ad:
#> [1] A B C
#> 
#> $vertices[[2]]
#> + 2/6 vertices, named, from c4da9ad:
#> [1] A F
#> 
#> 
#> $edges
#> $edges[[1]]
#> + 3/9 edges from c4da9ad (vertex names):
#> [1] A->B B->C C->A
#> 
#> $edges[[2]]
#> + 2/9 edges from c4da9ad (vertex names):
#> [1] F->A A->F
#> 
#>