Graphical models are intuitive tools to demonstrate dependence relation between variables of interest. Both undirected and directed graphical models are widely used in many applications, such as reconstructing gene expression/co-expression networks and brain functional networks. A popular model for undirected graphs is the Gaussian graphical model, where conditional independence can be inferred from the absence of an edge in the graph. Another approach for estimating undirected graphs does not depend on the distribution of the data. Instead, the resulting network is constructed through transformation of empirical sample correlation and node connectivity. The estimated network connectivity measures can be used as a secondary phenotype for association tests with genotypes. Finally, new methods have been proposed to estimate directed Gaussian graphs. The direction of an edge allows easier interpretation of causal relation between nodes in the graph. We first aim to estimate multiple Gaussian graphs in the presence of sample heterogeneity, where the independent samples may come from different and unknown populations or distributions. We embed in the framework of a Gaussian mixture model one of two recently proposed methods for estimating multiple precision matrices in Gaussian graphical models. Secondly, we adapt a weighted gene co-expression network analysis (WGCNA) framework to resting-state fMRI (rs-fMRI) data to identify modular structures in brain functional networks. We propose applying a new adaptive test built on the proportional odds model (POM) that can be applied to a high-dimensional setting, where the number of variables (p) can exceed the sample size (n) in addition to the usual p < n setting. Finally, we implemented a new method for estimating directed acyclic graph (DAG) as an R package, and demonstrated its use via application to a real data set and simulation studies.