There's a rather significant difference between the "network structure of eQTL" analysis (CONDOR, etc.), and performing functional annotation. The latter is ideally a bit more strict, and really needs to incorporate fine mapping. Specifically, for a single tissue, an "edge" would reflect whether a SNP is in the credible set for the expression of a gene (see https://www.nature.com/articles/s41467-021-23134-8#Sec9).
It seems like you're interested in tissue specific effects; in which case the fine-mapping model should be updated to be of the form
expression ~ tissue + genotype_i + tissue:genotype_i
and ask for whether the SNP is in the credible set for the cross-term. Note that you do have to be careful; as a variant which has a strong effect in all tissues except one will look like a specific-effect (in the opposite direction) for that tissue.
Note that in the limit of infinite data, every tissue will necessarily have a tissue-specific term, if only due to pure cell compositional effects, so a general methodology probably won't answer particular questions about tissue-specific action of regulatory variants (which typically would take the form of a contrast, e.g., "stronger in intestine than stomach").
That said, a good entry-point for bipartite network analysis might be https://europepmc.org/article/pmc/6333914. Bipartite networks occur regularly in:
miRNA targets: (miRNA, RNA) edges
drug targets: (drug, predicted binding target) edges
receptor-ligand interactions: (receptor, ligand) edges
TF-gene networks: (TF, regulated gene) edges
so literature in all of these areas could provide inspiration for the analysis you might want to perform.