Max function

Maximisation for graphs

Max generates a maximal graph that induces the same independence model from a non-maximal graph.

Max(amat)

Arguments

• amat: An adjacency matrix, or a graph that can be a graphNEL or an igraph object or a vector of length $3e$, where $e$ is the number of edges of the graph, that is a sequence of triples (type, node1label, node2label). The type of edge can be "a" (arrows from node1 to node2), "b" (arcs), and "l" (lines).

Details

Max looks for non-adjacent pais of nodes that are connected by primitive inducing paths, and connect such pairs by an appropriate edge.

Returns

A matrix that consists 4 different integers as an $ij$-element: 0 for a missing edge between $i$ and $j$, 1 for an arrow from $i$ to $j$, 10 for a full line between $i$ and $j$, and 100 for a bi-directed arrow between $i$ and $j$. These numbers are added to be associated with multiple edges of different types. The matrix is symmetric w.r.t full lines and bi-directed arrows.

References

Richardson, T.S. and Spirtes, P. (2002). Ancestral graph Markov models. Annals of Statistics, 30(4), 962-1030.

Sadeghi, K. and Lauritzen, S.L. (2014). Markov properties for loopless mixed graphs. Bernoulli 20(2), 676-696.

Author(s)

Kayvan Sadeghi

See Also

MAG, MRG, msep, MSG

Examples

H <- matrix(c(  0,100,  1,  0,
                  100,  0,100,  0,
                    0,100,  0,100,
                    0,  1,100,  0), 4, 4)
Max(H)