  Gaussian graphical models emerge in a wide range of fields. They model the
statistical relationships between variables as a graph, where an edge between
two variables indicates conditional dependence. Unfortunately, well-established
estimators, such as the graphical lasso or neighborhood selection, are known to
be susceptible to a high prevalence of false edge detections. False detections
may encourage inaccurate or even incorrect scientific interpretations, with
major implications in applications, such as biomedicine or healthcare. In this
paper, we introduce a nodewise variable selection approach to graph learning
and provably control the false discovery rate of the selected edge set at a
self-estimated level. A novel fusion method of the individual neighborhoods
outputs an undirected graph estimate. The proposed method is parameter-free and
does not require tuning by the user. Benchmarks against competing false
discovery rate controlling methods in numerical experiments considering
different graph topologies show a significant gain in performance.
