Cataloging the association of transcripts to genetic variants in recent years holds the promise for functional dissection of regulatory structure of human transcription. Here, we present a novel approach, which aims at elucidating the joint relationships between transcripts and single-nucleotide polymorphisms (SNPs). This entails detection and analysis of modules of transcripts, each weakly associated to a single genetic variant, together exposing a high-confidence association signal between the module and this 'main' SNP. To explore how transcripts in a module are related to causative loci for that module, we represent such dependencies by a graphical model. We applied our method to the existing data on genetics of gene expression in the liver. The modules are significantly more, larger and denser than found in permuted data. Quantification of the confidence in a module as a likelihood score, allows us to detect transcripts that do not reach genome-wide significance level. Topological analysis of each module identifies novel insights regarding the flow of causality between the main SNP and transcripts. We observe similar annotations of modules from two sources of information: the enrichment of a module in gene subsets and locus annotation of the genetic variants. This and further phenotypic analysis provide a validation for our methodology.