Understanding how neuronal networks reorganize in response to external stimuli and give rise to behavior is a central challenge in neuroscience and artificial intelligence. However, existing methods often fail to capture the evolving structure of neural connectivity in ways that capture its relationship to behavior, especially in dynamic, uncertain, or high-dimensional settings with sufficient resolution or interpretability. We introduce the Temporal Attention-enhanced Variational Graph Recurrent Neural Network (TAVRNN), a novel framework that models time-varying neuronal connectivity by integrating probabilistic graph learning with temporal attention mechanisms. TAVRNN learns latent dynamics at the single-unit level while maintaining interpretable population-level representations, to identify key connectivity patterns linked to behavior. TAVRNN generalizes across diverse neural systems and modalities, demonstrating state-of-the-art classification and clustering performance. We validate TAVRNN on three diverse datasets: (1) electrophysiological data from a freely behaving rat, (2) primate somatosensory cortex recordings during a reaching task, and (3) biological neurons in the DishBrain platform interacting with a virtual game environment. Our method outperforms state-of-the-art dynamic embedding techniques, revealing previously unreported relationships between adaptive behavior and the evolving topological organization of neural networks. These findings demonstrate that TAVRNN offers a powerful and generalizable approach for modeling neural dynamics across experimental and synthetic biological systems. Its architecture is modality-agnostic and scalable, making it applicable across a wide range of neural recording platforms and behavioral paradigms.