R: Chordality of a graph

is_chordal {igraph} | R Documentation

## Chordality of a graph

### Description

A graph is chordal (or triangulated) if each of its cycles of four or more nodes has a chord, which is an edge joining two nodes that are not adjacent in the cycle. An equivalent definition is that any chordless cycles have at most three nodes.

### Usage

    is_chordal(
      graph,
      alpha = NULL,
      alpham1 = NULL,
      fillin = FALSE,
      newgraph = FALSE
    )

### Arguments

`graph` | The input graph. It may be directed, but edge directions are ignored, as the algorithm is defined for undirected graphs.
`alpha` | Numeric vector, the maximal chardinality ordering of the vertices. If it is `NULL`, then it is automatically calculated by calling `max_cardinality`, or from `alpham1` if that is given..
`alpham1` | Numeric vector, the inverse of `alpha`. If it is `NULL`, then it is automatically calculated by calling `max_cardinality`, or from `alpha`.
`fillin` | Logical scalar, whether to calculate the fill-in edges.
`newgraph` | Logical scalar, whether to calculate the triangulated graph.

### Details

The chordality of the graph is decided by first performing maximum cardinality search on it (if the `alpha` and `alpham1` arguments are `NULL`), and then calculating the set of fill-in edges.

The set of fill-in edges is empty if and only if the graph is chordal.

It is also true that adding the fill-in edges to the graph makes it chordal.

### Value

A list with three members:

`chordal` | Logical scalar, it is `TRUE` iff the input graph is chordal.
`fillin` | If requested, then a numeric vector giving the fill-in edges. `NULL` otherwise.
`newgraph` | If requested, then the triangulated graph, an `igraph` object. `NULL` otherwise.

### Author(s)

Gabor Csardi csardi.gabor@gmail.com

### References

Robert E Tarjan and Mihalis Yannakakis. (1984). Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal of Computation 13, 566–579.

### See Also

`max_cardinality`

### Examples

    ## The examples from the Tarjan-Yannakakis paper
    g1 <- graph_from_literal(A-B:C:I, B-A:C:D, C-A:B:E:H, D-B:E:F,
                    E-C:D:F:H, F-D:E:G, G-F:H, H-C:E:G:I,
                    I-A:H)
    max_cardinality(g1)
    is_chordal(g1, fillin=TRUE)

    g2 <- graph_from_literal(A-B:E, B-A:E:F:D, C-E:D:G, D-B:F:E:C:G,
                    E-A:B:C:D:F, F-B:D:E, G-C:D:H:I, H-G:I:J,
                    I-G:H:J, J-H:I)
    max_cardinality(g2)
    is_chordal(g2, fillin=TRUE)

[Package igraph version 1.3.1 Index]