One Shared Graph, Two Mappings: Bidirectional Graph Autoencoder for Brain Structural and Functional Connectivity

Structural connectivity (SC) derived from diffusion MRI and functional connectivity (FC) derived from functional MRI provide complementary summaries of brain organization across large-scale networks. Because coherent brain function is supported by anatomically grounded, polysynaptic communication pathways, we model SC and FC as arising from a shared, biologically meaningful scaffold and propose a bidirectional graph autoencoder to estimate a shared latent graph common to both modalities. The method fits jointly trained forward and reverse mappings (SC$\to$FC and FC$\to$SC) that share a single latent adjacency matrix, which serves as the propagation operator for message passing in both modalities and links the two directions through a common graph over brain regions. On the landmark Human Connectome Project (HCP) and Adolescent Brain Cognitive Development (ABCD) data, the proposed approach improves both bidirectional reconstruction accuracy and graph reliability over existing graph-based and connectome translation methods, yielding roughly 7%-15% lower reconstruction error and about 4%-16% higher top-edge overlap. Moreover, the learned graphs exhibit strong cross-cohort consistency between HCP and ABCD, supporting the utility of the framework for interpretable brain structure-function modeling.