is_chordal
Chordality of a graph
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.
- Keywords
- graphs
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 callingmax_cardinality, or fromalpham1if that is given..- alpham1
Numeric vector, the inverse of
alpha. If it isNULL, then it is automatically calculated by callingmax_cardinality, or fromalpha.- 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:
Logical scalar, it is
TRUE iff the input graph is chordal.
If requested,
then a numeric vector giving the fill-in edges. NULL otherwise.
If requested, then the triangulated graph, an igraph
object. NULL otherwise.
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
Examples
# NOT RUN {
## 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)
# }