Conceptualization of different aspects of cloud applications and formal representations of interactions among the different components of SaaS are most crucial issues towards the design of an effective cloud architectural framework. In this paper a graph-based specification called Cloud Service Architecture Graph (CSAG) has been proposed to model such interactions among various components of Software as a Service (SaaS). CSAG is capable of addressing several important aspects like extendibility, composability, analyzability etc. for SaaS based applications over cloud environment. Moreover, several properties of CSAG shows that the proposed approach is effective towards the design of a SaaS based applications. The proposed CSAG has been illustrated using the case study of Electronic Health Record (EHR) system over cloud environment. © 2014 IEEE.