Gaussian graphical model ($\Omega ={\Sigma }^{-1},{\Omega }_{jk}=0⟺\{j,k\}\notin E$)

For a nondegenerate multivariate normal distribution, the conditional independence graph is read from zeros in its precision matrix. Conditional independence of two components given all others is equivalent to a zero cross term in their conditional Gaussian quadratic density, hence to ${\Omega }_{jk}=0$. It does not generally correspond to a zero in the covariance matrix.