The analysis of biophysical neural networks (BNNs) has been a longstanding focus in computational neuroscience. A central yet unresolved challenge in BNN analysis lies in deciphering the correlations between neuronal and synaptic dynamics, their connectivity patterns, and learning process. To address this, we introduce a novel BNN analysis framework grounded in network representation learning (NRL), which leverages attention scores to uncover intricate correlations between network components and their features. Our framework integrates a new computational graph (CG)-based BNN representation, a bio-inspired graph attention network (BGAN) that enables multiscale correlation analysis across BNN representations, and an extensive BNN dataset. The CG-based representation captures key computational features, information flow, and structural relationships underlying neuronal and synaptic dynamics, while BGAN reflects the compositional structure of neurons, including dendrites, somas, and axons, as well as bidirectional information flows between BNN components. The dataset comprises publicly available models from ModelDB, reconstructed using the Python and standardized in NeuroML format, and is augmented with data derived from canonical neuron and synapse models. To our knowledge, this study is the first to apply an NRL-based approach to the full spectrum of BNNs and their analysis.