Business Architecture (BA) plays a significant role in helping organizations understand enterprise structures and processes, and align them with strategic objectives. However, traditional BAs are represented in fixed structure with static model elements and fail to dynamically capture business insights based on internal and external data. To solve this problem, this paper introduces the graph theory into BAs with aim of building extensible data-driven analytics and automatically generating business insights. We use IBM's Component Business Model (CBM) as an example to illustrate various ways in which graph theory can be leveraged for data-driven analytics, including what and how business insights can be obtained. Future directions for applying graph theory to business architecture analytics are discussed.