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Fundamental cycles of a spanning tree

fundamental_cycles.Rd

Returns the fundamental cycles of a spanning tree with respect to the original graph. There is one fundamental cycle per non-tree edge (m - n + 1 total), formed by adding that edge to the unique path between its endpoints in the spanning tree.

Usage

fundamental_cycles(graph, tree)

Arguments

graph

An adj object representing a connected undirected graph.

tree

An adj object representing a spanning tree of graph.

Value

A list of adj objects, one per non-tree edge. Each adj represents the cycle as a subgraph of graph.

See also

fundamental_cuts()

Examples

g <- adj::adj(list(c(2L, 3L), c(1L, 3L), c(1L, 2L)))
t <- minimum_spanning_tree(g)
fundamental_cycles(g, t)
#> [[1]]
#> <adj[3]>
#> [1] {2, 3} {1, 3} {1, 2}
#>