Music is inherently made up of complex structures, and representing them as graphs helps to capture multiple levels of relationships. While music generation has been explored using various deep generation techniques, research on graph-related music generation is sparse. Earlier graph-based music generation worked only on generating melodies, and recent works to generate polyphonic music do not account for longer-term structure. In this paper, we explore a multi-graph approach to represent both the rhythmic patterns and phrase structure of Chinese pop music. Consequently, we propose a two-step approach that aims to generate polyphonic music with coherent rhythm and long-term structure. We train two Variational Auto-Encoder networks - one on a MIDI dataset to generate 4-bar phrases, and another on song structure labels to generate full song structure. Our work shows that the models are able to learn most of the structural nuances in the training dataset, including chord and pitch frequency distributions, and phrase attributes.