Maximal prime subgraph decomposition

Finding a junction tree representation of the MPD (maximal prime subgraph decomposition) of an undirected graph The maximal prime subgraph decomposition of a graph is the smallest subgraphs into which the graph can be decomposed.

mpd(object, tobject = minimal_triang(object), details = 0)

# Default S3 method
mpd(object, tobject = triangulate(object), details = 0)

mpdMAT(amat, tamat = minimal_triangMAT(amat), details = 0)

Arguments

object

An undirected graph; a graphNEL object, an igraph or an adjacency matrix.

tobject

Any minimal triangulation of object; a graphNEL object, an igraph or an adjacency matrix.

details

The amount of details to be printed.

amat

An undirected graph; a symmetric adjacency matrix

tamat

Any minimal triangulation of object; a symmetric adjacency matrix

Value

A list with components "nodes", "cliques", "separators", "parents", "children", "nLevels". The component "cliques" defines the subgraphs.

References

Kristian G. Olesen and Anders L. Madsen (2002): Maximal Prime Subgraph Decomposition of Bayesian Networks. IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, PART B: CYBERNETICS, VOL. 32, NO. 1, FEBRUARY 2002

See also

mcs, mcsMAT, minimal_triang, minimal_triangMAT, rip, ripMAT, triangulate, triangulateMAT

Author

Clive Bowsher C.Bowsher@statslab.cam.ac.uk with modifications by Søren Højsgaard, sorenh@math.aau.dk

Examples

## Maximal prime subgraph decomposition - a graphNEL object
g1 <- ug(~ a:b + b:c + c:d + d:e + e:f + a:f + b:e)
if (interactive()) plot(g1)
x <- mpd(g1)

## Maximal prime subgraph decomposition - an adjacency matrix
g1m <- ug(~ a:b + b:c + c:d + d:e + e:f + a:f + b:e, result="matrix")
if (interactive()) plot(as(g1m, "graphNEL"))
x <- mpdMAT(g1m)