Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior accounts for degree heterogeneity edge sparsity, and graph topology the graph. The resulting posterior distribution is incorporated into a multiple testing procedure for graph inference with false discovery rate control. Computation is carried out through a combination of adaptive elastic nets and a variational expectation--maximization algorithm. In simulations, the method achieves reliable false discovery rate control while maintaining strong power, especially in heterogeneous networks such as graphs with hubs, and remains competitive under structural misspecification. Applications to breast cancer gene expression data and financial return networks show that the method yields sparse and interpretable conditional dependence graphs while retaining the most stable interactions detected by competing approaches.

翻译：从高维高斯数据中估计条件独立图具有挑战性，因为方法需在检测相关边的同时严格统计控制误差。我们提出一个基于先验项的贝叶斯框架，该先验项兼顾了节点度异质性、边稀疏性与图拓扑结构。由此得到的后验分布被整合进一个用于图推断的多重检验流程中，并实现了错误发现率控制。计算过程通过自适应弹性网与变分期望最大化算法相结合完成。在模拟实验中，本方法在保持较强功效的同时实现了可靠的控制错误发现率，特别是在异质性网络（如包含枢纽节点的图）中表现突出，并且在结构设定错误的情况下仍具竞争力。乳腺癌基因表达数据与金融收益网络的应用表明，该方法能在保留竞争方法所检测到的最稳定相互作用的同时，生成稀疏且可解释的条件依赖图。