We propose a new methodology based on graph theory for selecting high priority "anchor areas" to which conservation and restoration activities could be "attached", in order to maximize the impact of the available resources on biodiversity conservation and on increasing the landscape functional connectivity. Anchor areas are defined as habitat fragments which are among the largest present in the landscape and the most important for maintaining the landscape functional connectivity, as quantified by the Integral Index of Connectivity (IIC). Recommended actions include increasing the protection of the anchor areas and restoring smaller fragments in their neighborhood whose size and placement make them convenient "stepping stones" in the establishment of ecological corridors between the anchor areas and other areas with a potentially high biological importance. We illustrate our approach with an analysis of the sizes and functional connections between remaining forest fragments in the "Mesopotamia of Biodiversity", a portion of Brazilian Atlantic Forest with an especially rich biodiversity situated between the rivers Jequitinhonha and Doce.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)