The explorations of brain functional connectivity (FC) network using resting-state functional magnetic resonance imaging (rs-fMRI) can provide crucial insights into discriminative analysis of neuropsychiatric disorders such as schizophrenia (SZ). Graph attention network (GAT), which could capture the local stationary on the network topology and aggregate the features of neighboring nodes, has advantages in learning the feature representation of brain regions. However, GAT only can obtain the node-level features that reflect local information, ignoring the spatial information within the connectivity-based features that proved to be important for SZ diagnosis. In addition, existing graph learning techniques usually rely on a single graph topology to represent neighborhood information, and only consider a single correlation measure for connectivity features. Comprehensive analysis of multiple graph topologies and multiple measures of FC can leverage their complementary information that may contribute to identifying patients. In this paper, we propose a multi-graph attention network (MGAT) with bilinear convolution (BC) neural network framework for SZ diagnosis and functional connectivity analysis. Besides multiple correlation measures to construct connectivity networks from different perspectives, we further propose two different graph construction methods to capture both the low- and high-level graph topologies, respectively. Especially, the MGAT module is developed to learn multiple node interaction features on each graph topology, and the BC module is utilized to learn the spatial connectivity features of the brain network for disease prediction. Importantly, the rationality and advantages of our proposed method can be validated by the experiments on SZ identification. Therefore, we speculate that this framework may also be potentially used as a diagnostic tool for other neuropsychiatric disorders.