The　neuroscience　community　has　developed　many　convolutional　neural　networks　(CNNs)　for　the　early　detection　of　Alzheimer＇s　disease　(AD).　Population　graphs　are　thought　of　as　non-linear　structures　that　capture　the　relationships　between　individual　subjects　represented　as　nodes,　which　allows　for　the　simultaneous　integration　of　imaging　and　non-imaging　information　as　well　as　individual　subjects＇　features.　Graph　convolutional　networks　(GCNs)　generalize　convolution　operations　to　accommodate　non-Euclidean　data　and　aid　in　the　mining　of　topological　information　from　the　population　graph　for　a　disease　classification　task.　However,　few　studies　have　examined　how　GCNs＇　input　properties　affect　AD-staging　performance.　Therefore,　we　conducted　three　experiments　in　this　work.　Experiment　1　examined　how　the　inclusion　of　demographic　information　in　the　edge-assigning　function　affects　the　classification　of　AD　versus　cognitive　normal　(CN).　Experiment　2　was　designed　to　examine　the　effects　of　adding　various　neuropsychological　tests　to　the　edge-assigning　function　on　the　mild　cognitive　impairment　(MCI)　classification.　Experiment　3　studied　the　impact　of　the　edge　assignment　function.　The　best　result　was　obtained　in　Experiment　2　on　multi-class　classification　(AD,　MCI,　and　CN).　We　applied　a　novel　framework　for　the　diagnosis　of　AD　that　integrated　CNNs　and　GCNs　into　a　unified　network,　taking　advantage　of　the　excellent　feature　extraction　capabilities　of　CNNs　and　population-graph　processing　capabilities　of　GCNs.　To　learn　high-level　anatomical　features,　DenseNet　was　used;　a　set　of　population　graphs　was　represented　with　nodes　defined　by　imaging　features　and　edge　weights　determined　by　different　combinations　of　imaging　or/and　non-imaging　information,　and　the　generated　graphs　were　then　fed　to　the　GCNs　for　classification.　Both　binary　classification　and　multi-class　classification　showed　improved　performance,　with　an　accuracy　of　91.6%　for　AD　versus　CN,　91.2%　for　AD　versus　MCI,　96.8%　for　MCI　versus　CN,　and　89.4%　for　multi-class　classification.　The　population　graph＇s　imaging　features　and　edge-assigning　functions　can　both　significantly　affect　classification　accuracy.