Computational drug repositioning approaches should be investigated for the identification of new treatments for Alzheimer's patients as a huge amount of omics data has been produced during pre-clinical and clinical studies. Here, we investigated a gene network in Alzheimer's patients to detect a proper therapeutic target. We screened the targets of different drugs (34,006 compounds) using data available in the Connectivity Map database. Then, we analyzed transcriptome profiles of Alzheimer's patients to discover a network of gene-drugs based on mutual information, representing an index of dependence among genes. This study identified a network consisting of 25 genes and compounds and interconnected biological processes using computational approaches. The results also highlight the diagnostic role of the 25 genes since we obtained good classification performances using a neural network model. We also suggest 12 repurposable drugs (like KU-60019, AM-630, CP55940, enflurane, ginkgolide B, linopirdine, apremilast, ibudilast, pentoxifylline, roflumilast, acitretin, and tamibarotene) interacting with 6 genes (ATM, CNR1, GLRB, KCNQ2, PDE4B, and RARA), that we linked to retrograde endocannabinoid signaling, synaptic vesicle cycle, morphine addiction, and homologous recombination.