The volume of the manifold is a geometric characteristic associated with the topology of Bayesian network. Each BN produces a different magnitude of the volume based on the DAG of Bayesian network.
Collapse, Line, Star, PseudoLoop, Diamond, Rhombus.
References
Eitel J. M. L., (2008), An Information-geometric approach to learning Bayesian network topologies from data, Innovations in Bayesian Networks Studies in Computational Intelligence, Vol. 156, 187-217.