The traditional approach to business process modelling frequently results in large models that are difficult to change and maintain. In cloud-based environment, business dynamics are mandating that business processes normally be increasingly responsive to changes. This demands business process should be highly modular, scalable and flexible for cloud-based applications. Further, in cloud-based business environments, besides describing new capabilities, process models should also define how those capabilities can be integrated with the existing systems. In this paper, a hierarchical graph-based specification called business component graph for SaaS (BCGS) has been proposed to address those issues. The proposed BCGS, formally, realises the business components for software as a service (SaaS)-based applications. BCGS represents the complex business logic design as a set of business components and their inter-relationships. Here, business component is defined as methodical integration of business processes and business rules. This proposed integration approach facilitates high scalability and reusability of constituent elements of business components and ensures the consistency between processes and business rules. Moreover, this paper also includes the service orientation of the proposed concepts in SaaS framework. A detailed case study of BCGS also has been illustrated to show the expressiveness of the proposed concepts.