AD is the highly severe part of the dementia spectrum and impairs cognitive abilities of individuals, bringing economic, societal and psychological burdens beyond the diseased. A promising approach in AD research is the analysis of structural and functional brain connectomes, i.e., sNETs and fNETs, respectively. We propose to use tensor representation (B-tensor) of uni-modal and multi-modal brain connectomes to define a low-dimensional space via tensor factorization. We show on a cohort of 47 subjects, spanning the spectrum of dementia, that diagnosis with an accuracy of 77% to 100% is achievable in a 5D connectome space using different structural and functional connectome constructions in a uni-modal and multi-modal fashion. We further show that multi-modal tensor factorization improves the results suggesting complementary information in structure and function. A neurological assessment of the connectivity patterns identified largely agrees with prior knowledge, yet also suggests new associations that may play a role in the disease progress.