With the Big Data of culture, network science is advancing the arts and humanities by exploring the innate patterns in the data and interpreting the significance in their own fields. In this paper we apply network science to understand associations between the composers of western classical music constructed from comprehensive data of classical music CD recordings. First, we study the topology of the network to uncover the characteristics of the large-scale composer--composer associations. We also investigate the topological evolution of our network to understand the development process of classical music composers in the industry. We believe that our study can afford novel insights into traditional musicology and can underline the potential of network science as a complementary framework for the arts and humanities.