Compute Possible-D-SEP(x,G) of a node x in a PDAG G


Let G be a graph with the following edge types: o-o, o-> or <->, and let x be a vertex in the graph. Then this function computes Possible-D-SEP(x,G), which is defined as follows:

v is in Possible-D-SEP(x,G) iff there is a path p between x and v in G such that for every subpath <s,t,u> of p, t is a collider on this subpath or <s,t,u> is a triangle in G.

See Spirtes et al (2000) or Definition 3.3 of Colombo et al (2012).


  qreach(x, amat, verbose = FALSE)



(integer) position of vertex x in the adjacency matrix of which Possible-D-SEP set is to be computed.


Adjacency matrix of type amat.pag.


Logical, asking for details on output


Vector of column positions indicating the nodes in Possible-D-SEP of x.


Markus Kalisch (


P. Spirtes, C. Glymour and R. Scheines (2000). Causation, Prediction, and Search, 2nd edition, The MIT Press.

D. Colombo, M.H. Maathuis, M. Kalisch, T.S. Richardson (2012). Learning high-dimensional directed acyclic graphs with latent and selection variables. Annals of Statistics 40, 294–321.

See Also

fci and pdsep which both use this function.

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