Many methods have been proposed in the literature for diagnosis of Alzheimer's disease (AD) in the early stages, among which the graph-based methods have been more popular, because of their capability to utilize the relational information among different brain regions. Here, we design a novel graph signal processing based integrated AD detection model using multimodal deep learning that simultaneously utilizes both the static and the dynamic brain connectivity based features extracted from resting-state fMRI (rs-fMRI) data to detect AD in the early stages. First, our earlier proposed state-space model (SSM) based graph connectivity dynamics characterization method is used to design a modified dynamic connectivity based AD detection model. After verifying its utility, this dynamic connectivity based model is integrated with our earlier designed static connectivity based AD detection model using the intermediate level integration approach of the multimodal deep learning, to construct our proposed integrated AD detection model. To verify the effectiveness of the designed AD detection models, the models are applied on the rs-fMRI data, extracted from ADNI dataset. Superior performance of our proposed AD diagnosis method corroborates its utility in AD detection application.