  A Bayesian Network (BN) is a probabilistic model that represents a set of
variables using a directed acyclic graph (DAG). Current algorithms for learning
BN structures from data focus on estimating the edges of a specific DAG, and
often lead to many `likely' network structures. In this paper, we lay the
groundwork for an approach that focuses on learning global properties of the
DAG rather than exact edges. This is done by defining the structural hypergraph
of a BN, which is shown to be related to the inverse-covariance matrix of the
network. Spectral bounds are derived for the normalized inverse-covariance
matrix, which are shown to be closely related to the maximum indegree of the
associated BN.
