igraph: is_chordal – R documentation

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is_chordal

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.

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)

igraph

Network Analysis and Visualization

v1.2.10

GPL (>= 2)

Authors

See AUTHORS file.

Initial release