The Tian decomposition of a mixed graph G allows one to globally identify the covariance matrices Sigma' of special subgraphs of G called c-components. This function takes the covariance matrix Sigma corresponding to G and a collection of node sets which specify the c-component, and returns the Sigma' corresponding to the c-component.
tianSigmaForComponent(Sigma, internal, incoming, topOrder)the new Sigma corresponding to the c-component
the covariance matrix for the mixed graph G
an integer vector corresponding to the vertices of the C-component that are in the bidirected equivalence classes (if the graph is not-acyclic then these equivalence classes must be enlarged by combining two bidirected components if there are two vertices, one in each component, that are simultaneously on the same directed cycle).
the parents of vertices in internal that are not in the set internal themselves
a topological ordering of c(internal, incoming) with respect to the graph G. For vertices in a strongly connected component the ordering is allowed to be arbitrary.