Measurement of well-being has been a highly debated topic since the end of the last century. While some specific aspects are still open issues, a multidimensional approach as well as the construction of shared and well-rooted systems of indicators are now accepted as the main route to measure this complex phenomenon. A meaningful effort, in this direction, is that of the Italian "Equitable and Sustainable Well-being" (BES) system of indicators, developed by the Italian National Institute of Statistics (ISTAT) and the National Council for Economics and Labour (CNEL). The BES framework comprises a number of atomic indicators measured yearly at the regional level and reflecting the different domains of well-being (e.g. Health, Education, Work \& Life Balance, Environment,...). In this work we aim at dealing with the multidimensionality of the BES system of indicators and try to answer three main research questions: I) What is the structure of the relationships among the BES atomic indicators; II) What is the structure of the relationships among the BES domains; III) To what extent the structure of the relationships reflects the current BES theoretical framework. We address these questions by implementing Bayesian Networks (BNs), a widely accepted class of multivariate statistical models, particularly suitable for handling reasoning with uncertainty. Implementation of a BN results in a set of nodes and a set of conditional independence statements that provide an effective tool to explore associations in a system of variables. In this work, we also suggest two strategies for encoding prior knowledge in the BN estimating algorithm so that the BES theoretical framework can be represented into the network.