Independency Relationships in Singly Connected Networks

Graphical structures such as causal networks or Markov networks are very useful tools for representing irrelevance or independency relationships. Singly connected networks are important speciic cases where there is no more than one undirected path connecting each pair of variables. The aim of this paper is to investigate the kind of properties that a dependency model must verify in order to be equivalent to a singly connected graph structure, either via the d-separation criterion for directed acyclic graphs or via the separation criterion for undirected graphs. The main results are the characterizations of those dependency models which are isomorphic to singly connected graphs, as well as the development of eecient algorithms for learning singly connected graph representations of dependency models.