The connectional brain template (CBT) captures the shared traits across all individuals of a given population of brain connectomes, thereby acting as a fingerprint. Estimating a CBT from a population where brain graphs are derived from diverse neuroimaging modalities (e.g., functional and structural) and at different resolutions (i.e., number of nodes) remains a formidable challenge to solve. Such network integration task allows for learning a rich and universal representation of the brain connectivity across varying modalities and resolutions. The resulting CBT can be substantially used to generate entirely new multimodal brain connectomes, which can boost the learning of the downs-stream tasks such as brain state classification. Here, we propose the Multimodal Multiresolution Brain Graph Integrator Network (i.e., M2GraphIntegrator), the first multimodal multiresolution graph integration framework that maps a given connectomic population into a well centered CBT. M2GraphIntegrator first unifies brain graph resolutions by utilizing resolution-specific graph autoencoders. Next, it integrates the resulting fixed-size brain graphs into a universal CBT lying at the center of its population. To preserve the population diversity, we further design a novel clustering-based training sample selection strategy which leverages the most heterogeneous training samples. To ensure the biological soundness of the learned CBT, we propose a topological loss that minimizes the topological gap between the ground-truth brain graphs and the learned CBT. Our experiments show that from a single CBT, one can generate realistic connectomic datasets including brain graphs of varying resolutions and modalities. We further demonstrate that our framework significantly outperforms benchmarks in reconstruction quality, augmentation task, centeredness and topological soundness.