Neurodegenerative diseases affect brain morphology and connectivity, making complex networks a suitable tool to investigate and model their effects. Because of its stereotyped pattern Alzheimer’s disease (AD) is a natural benchmark for the study of novel methodologies. Several studies have investigated the network centrality and segregation changes induced by AD, especially with a single subject approach. In this work, a holistic perspective based on the application of multiplex network concepts is introduced. We define and assess a diagnostic score to characterize the brain topology and measure the disease effects on a mixed cohort of 52 normal controls (NC) and 47 AD patients, from Alzheimer’s Disease Neuroimaging Initiative (ADNI). The proposed topological score allows an accurate NC-AD classification: the average area under the curve (AUC) is 95% and the 95% confidence interval is 92%–99%. Besides, the combination of topological information and structural measures, such as the hippocampal volumes, was also investigated. Topology is able to capture the disease signature of AD and, as the methodology is general, it can find interesting applications to enhance our insight into disease with more heterogeneous patterns.