graph of pairwise frequencies with which two genes are assigned to the same gene module [@bonnet2015].

Causal gene networks
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Using genotype data to prioritize edge directions in co-expression networks\[sec-direction\]
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Pairwise correlations between gene expression traits define undirected co-expression networks. Several studies have shown that pairs of gene expression traits can be causally ordered using genotype data [@zhu2004; @chen2007harnessing; @aten2008using; @schadt2005integrative; @neto2008inferring; @neto2013modeling; @millstein2009disentangling]. Although varying in their statistical details, these methods conclude that gene $A$ is causal for gene $B$, if expression of $B$ associates significantly with $A$’s eQTLs and this association is abolished by conditioning on expression of $A$ and on any other known confounding factors. In essence, this is the principle of “Mendelian randomization”, first introduced in epidemiology as an experimental design to detect causal effects of environmental exposures on human health [@smith2003mendelian], applied to gene expression traits.

To illustrate how these methods work, let $A$ and $B$ be two random variables representing two gene expression traits, and let $E$ be a random variable representing a SNP which is an eQTL for gene $A$ and $B$. Since genotype cannot be altered by gene expression (i.e. $E$ cannot have any incoming edges), there are three possible regulatory 