  We consider a method to jointly estimate sparse precision matrices and their
underlying graph structures using dependent high-dimensional datasets. We
present a penalized maximum likelihood estimator which encourages both sparsity
and similarity in the estimated precision matrices where tuning parameters are
automatically selected by controlling the expected number of false positive
edges. We also incorporate an extra step to remove edges which represent an
overestimation of triangular motifs. We conduct a simulation study to show that
the proposed methodology presents consistent results for different combinations
of sample size and dimension. Then, we apply the suggested approaches to a
high-dimensional real case study of gene expression data with samples in two
medical conditions, healthy and colon cancer tissues, to estimate a common
network of genes as well as the differentially connected genes that are
important to the disease. We find denser graph structures for healthy samples
than for tumor samples, with groups of genes interacting together in the shape
of clusters.
