  We derive standard imsets for undirected graphical models and chain graphical
models. Standard imsets for undirected graphical models are described in terms
of minimal triangulations for maximal prime subgraphs of the undirected graphs.
For describing standard imsets for chain graphical models, we first define a
triangulation of a chain graph. We then use the triangulation to generalize our
results for the undirected graphs to chain graphs.
