Alzheimer’s disease (AD) is a neurodegenerative disorder characterized by a severe derangement of cognitive functions, primarily memory, in elderly subjects. As far as the functional impairment is concerned, growing evidence supports the disconnection syndrome hypothesis. Recent investigations using fMRI have revealed a generalized alteration of resting state networks in patients affected by AD and mild cognitive impairment (MCI). However, it was unclear whether the changes in functional connectivity were accompanied by corresponding structural network changes. In this work, we have developed a novel structural/functional connectomic approach: resting state fMRI was used to identify the functional cortical network nodes and diffusion MRI to reconstruct the fiber tracts to give a weight to internodal subcortical connections. Then, local and global efficiency were determined for different networks, exploring specific alterations of integration and segregation patterns in AD and MCI patients compared to healthy controls (HC). In the default mode network (DMN), that was the most affected, axonal loss and reduced axonal integrity appeared to compromise both local and global efficiency along posterior-anterior connections. In the basal ganglia network (BGN), disruption of white matter integrity implied that main alterations occurred in local microstructure. In the anterior insular network (AIN), neuronal loss probably subtended a compromised communication with the insular cortex. Cognitive performance, evaluated by neuropsychological examinations, revealed a dependency on integration and segregation of brain networks. These findings are indicative of the fact that cognitive deficits in AD could be associated not only with cortical alterations (revealed by fMRI) but also with subcortical alterations (revealed by diffusion MRI) that extend beyond the areas primarily damaged by neurodegeneration, towards the support of an emerging concept of AD as a disconnection syndrome. Since only AD but not MCI patients were characterized by a significant decrease in structural connectivity, integrated structural/functional connectomics could provide a useful tool for assessing disease progression from MCI to AD.