A major rise in the prevalence and impact of Alzheimer's disease (AD) is projected in the coming decades, resulting from increasing life expectancy, thus leading to substantially increased healthcare costs. While brain disfunctions at the time of diagnosis are irreversible, it is widely accepted that AD pathology develops decades before clinical symptoms onset. If incipient processes can be detected early in the disease progression, prospective intervention for preventing or slowing the disease can be designed. Currently, there is no noninvasive biomarker available to detect and monitor early stages of disease progression. The complex etiology of AD warrants a systems-based approach supporting the integration of multimodal and multilevel data, while network-based modeling provides the scaffolding for methods revealing complex systems-level disruptions initiated by the disease. In this work, we review current state-of-the-art, focusing on network-based biomarkers at molecular and brain functional connectivity levels. Particular emphasis is placed on outlining recent trends, which highlight the functional importance of modular substructures in molecular and connectivity networks and their potential biomarker value. Our perspective is rooted in network medicine and summarizes the pipelines for identifying network-based biomarkers, as well as the benefits of integrating genotype and brain phenotype information for a comprehensively noninvasive approach in the early diagnosis of AD. Finally, we propose a framework for integrating knowledge from molecular and brain connectivity levels, which has the potential to enable noninvasive diagnosis, provide support for monitoring therapies, and help understand heretofore unexamined deep level relations between genotype and brain phenotype.