essentialGraph {abn}  R Documentation 
Constructs different versions of the essential graph from a given DAG. External function that computes essential graph of a dag Minimal PDAG: The only directed edges are those who participate in vstructure Completed PDAG: very directed edge corresponds to a compelled edge, and every undirected edge corresponds to a reversible edge
essentialGraph(dag, node.names = NULL, PDAG = "minimal")
dag 
a matrix or a formula statement (see ‘Details’ for format) defining the network structure, a directed acyclic graph (DAG). 
node.names 
a vector of names if the DAG is given via formula, see ‘Details’. 
PDAG 
a character value that can be: minimal or complete, see ‘Details’. 
This function returns an essential graph from a DAG, aka acyclic partially directed graph (PDAG). This can be useful if the learning procedure is defined up to a Markov class of equivalence. A minimal PDAG is defined as only directed edges are those who participate in vstructure. Whereas the completed PDAG: every directed edge corresponds to a compelled edge, and every undirected edge corresponds to a reversible edge.
The dag
can be provided using a formula statement (similar to glm).
A typical formula is ~ node1parent1:parent2 + node2:node3parent3
.
The formula statement have to start with ~
.
In this example, node1 has two parents (parent1 and parent2).
node2 and node3 have the same parent3.
The parents names have to exactly match those given in node.names
.
:
is the separator between either children or parents,

separates children (left side) and parents (right side),
+
separates terms, .
replaces all the variables in node.names
.
A matrix giving the PDAG.
West, D. B. (2001). Introduction to Graph Theory. Vol. 2. Upper Saddle River: Prentice Hall. Chickering, D. M. (2013) A Transformational Characterization of Equivalent Bayesian Network Structures, arXiv:1302.4938.
dag < matrix(c(0,0,0, 1,0,0, 1,1,0), nrow = 3, ncol = 3)
dist < list(a="gaussian", b="gaussian", c="gaussian")
colnames(dag) < rownames(dag) < names(dist)
essentialGraph(dag)