Particulate composites underpin many solid-state chemical and electrochemical systems, where microstructural features such as multiphase boundaries and inter-particle connections strongly influence system performance. Advances in X-ray microscopy enable capturing large-scale, multimodal images of these complex microstructures with an unprecedentedly high throughput. However, harnessing these datasets to discover new physical insights and guide microstructure optimization remains a major challenge. Here, we develop a machine learning (ML) enabled framework that enables automated transformation of experimental multimodal X-ray images of multiphase particulate composites into scalable, topology-aware graphs for extracting physical insights and establishing local microstructure-property relationships at both the particle and network level. Using the multiphase particulate cathode of solid-state lithium batteries as an example, our ML-enabled graph analysis corroborates the critical role of triple phase junctions and concurrent ion/electron conduction channels in realizing desirable local electrochemical activity. Our work establishes graph-based microstructure representation as a powerful paradigm for bridging multimodal experimental imaging and functional understanding, and facilitating microstructure-aware data-driven materials design in a broad range of particulate composites.