A new method for model selection for Gaussian directed acyclic graphs (DAG) and Gaussian graphical models (GGM), with extensions towards ancestral graphs (AG), is constructed to have good prediction properties. The method is based on the focused information criterion, and offers the possibility of fitting individual tailored models. The focus of the research, that is, the purpose of the model, directs the selection. It is shown that using the focused information criterion leads to a graph with small mean square error. Two situations that commonly occur in practice are treated: the improvement of an already
pre-specified feasible model, and a data-driven full discovery of the graphical structure. The search algorithms are illustrated by means of data examples and are compared with existing methods in a simulation study.