Relationships among traits were investigated on the genomic and residual levels using novel methodology. This included inference on these relationships via Bayesian networks and an assessment of the networks with structural equation models. The methodology employed three steps. First, a Bayesian multiple-trait Gaussian model was fitted to the data to decompose phenotypic values into their genomic and residual components. Second, genomic and residual network structures among traits were learned from estimates of these two components. Network learning was performed using six different algorithmic settings for comparison, of which two were score-based and four were constraint-based approaches. Third, structural equation model analyses ranked the networks in terms of goodness of fit and predictive ability, and compared them with the standard multiple-trait fully recursive network. The methodology was applied to experimental data representing the European heterotic maize pools Dent and Flint (Zea mays L.). Inferences on genomic and residual trait connections were depicted separately as directed acyclic graphs. These graphs provide information beyond mere pairwise genetic or residual associations between traits, illustrating for example conditional independencies and hinting at potential causal links among traits. Network analysis suggested some genetic correlations as potentially spurious. Genomic and residual networks were compared between Dent and Flint.