graphmintriangulate  R Documentation 
An undirected graph uG is triangulated (or chordal) if it has no cycles of length >= 4 without a chord which is equivalent to that the vertices can be given a perfect ordering. Any undirected graph can be triangulated by adding edges to the graph, so called fillins which gives the graph TuG. A triangulation TuG is minimal if no fillins can be removed without breaking the property that TuG is triangulated.
minimal_triang( object, tobject = triangulate(object), result = NULL, details = 0 ) minimal_triangMAT(amat, tamat = triangulateMAT(amat), details = 0)
object 
An undirected graph represented either as a 
tobject 
Any triangulation of 
result 
The type (representation) of the result. Possible values are

details 
The amount of details to be printed. 
amat 
The undirected graph which is to be triangulated; a symmetric adjacency matrix. 
tamat 
Any triangulation of 
For a given triangulation tobject it may be so that some of the fillins are superflous in the sense that they can be removed from tobject without breaking the property that tobject is triangulated. The graph obtained by doing so is a minimal triangulation.
Notice: A related concept is the minimum triangulation, which is the the graph with the smallest number of fillins. The minimum triangulation is unique. Finding the minimum triangulation is NPhard.
minimal_triang()
returns a graphNEL object while
minimal_triangMAT()
returns an adjacency matrix.
Clive Bowsher C.Bowsher@statslab.cam.ac.uk with modifications by Søren Højsgaard, sorenh@math.aau.dk
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
mpd
, rip
, triangulate
## A graphNEL object g1 < ug(~a:b + b:c + c:d + d:e + e:f + a:f + b:e) x < minimal_triang(g1) ## g2 is a triangulation of g1 but it is not minimal g2 < ug(~a:b:e:f + b:c:d:e) x < minimal_triang(g1, tobject=g2) ## An adjacency matrix g1m < ug(~a:b + b:c + c:d + d:e + e:f + a:f + b:e, result="matrix") x < minimal_triangMAT(g1m)
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