# max_cardinality

##### Maximum cardinality search

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

- Keywords
- graphs

##### 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.

##### 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`

.

##### Value

A list with two components:

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

Numeric vector. The inverse of `alpha`

.

##### 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)
# }
```

*Documentation reproduced from package igraph, version 1.2.3, License: GPL (>= 2)*