  Expression quantitative trait loci (eQTL) mapping constitutes a challenging
problem due to, among other reasons, the high-dimensional multivariate nature
of gene-expression traits. Next to the expression heterogeneity produced by
confounding factors and other sources of unwanted variation, indirect effects
spread throughout genes as a result of genetic, molecular and environmental
perturbations. From a multivariate perspective one would like to adjust for the
effect of all of these factors to end up with a network of direct associations
connecting the path from genotype to phenotype. In this paper we approach this
challenge with mixed graphical Markov models, higher-order conditional
independences and q-order correlation graphs. These models show that additive
genetic effects propagate through the network as function of gene-gene
correlations. Our estimation of the eQTL network underlying a well-studied
yeast data set leads to a sparse structure with more direct genetic and
regulatory associations that enable a straightforward comparison of the genetic
control of gene expression across chromosomes. Interestingly, it also reveals
that eQTLs explain most of the expression variability of network hub genes.
