In this research project, we propose a model, the Harmony Graph, to decompose music into a social-network-like structure according to its harmonies. The whole Harmony Graph network represents the harmony progressions in music. The Harmony Graph is utilized to visualize, distinguish, and generate music for four prepared corpora using social network techniques. We experimented on different characteristics in social network analysis, and we found significant differences among the Harmony Graphs of the four corpora. A new measure called Agglomeration is created to characterize the agglomerating phenomenon that cannot be described sufficiently by existing measures. A corpus-based music composition method is also proposed in this research. By performing random-walk in a Harmony Graph, we generated new music that differs from yet reflects the style of music pieces in the corpus. With the link prediction technique, we also generated music more pleasant aurally than simply using random walks.