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The structure of a Bayesian network includes a great deal of informationabout the probability distribution of the data, which is uniquely identifiedgiven some general distributional assumptions. Therefore it's important tostudy its variability, which can be used to compare the performance ofdifferent learning algorithms and to measure the strength of any arbitrarysubset of arcs.  In this paper we will introduce some descriptive statistics and thecorresponding parametric and Monte Carlo tests on the undirected graphunderlying the structure of a Bayesian network, modeled as a multivariateBernoulli random variable. A simple numeric example and the comparison of theperformance of some structure learning algorithm on small samples will thenillustrate their use.

Measures of Variability for Bayesian Network Graphical Structures