Maximisation for graphs

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Description

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

Usage

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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.

Value

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.

Author(s)

Kayvan Sadeghi

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. (2011). Markov properties for loopless mixed graphs. Submitted. http://arxiv.org/abs/1109.5909.

See Also

MAG, MRG, msep, MSG

Examples

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

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