igraph (version 1.2.7)

max_cardinality: Maximum cardinality search

Description

Maximum cardinality search is a simple ordering a vertices that is useful in determining the chordality of a graph.

Usage

max_cardinality(graph)

Arguments

graph

The input graph. It may be directed, but edge directions are ignored, as the algorithm is defined for undirected graphs.

Value

A list with two components:

alpha

Numeric vector. The vertices ordered according to the maximum cardinality search.

alpham1

Numeric vector. The inverse of alpha.

Details

Maximum cardinality search visits the vertices in such an order that every time the vertex with the most already visited neighbors is visited. Ties are broken randomly.

The algorithm provides a simple basis for deciding whether a graph is chordal, see References below, and also is_chordal.

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

is_chordal

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)
# }