In the recent past, graph-based approaches have been proposed by various researchers for safety analysis and fault diagnosis of chemical process systems. Though these approaches have shown promise, there are a number of important issues that have not been adequately addressed in the literature. The issue of systematic development of graph representations for chemical processes has not been addressed in the literature. This is an important issue because the development of digraphs is error-prone and time-consuming. Further, little attention has been paid toward understanding the conceptual relationship between the underlying mathematical description and the analysis procedures for the graph model. Also, the utility of these graph-based approaches at a flowsheet level has not been studied. With these issues in perspective, in this first part of the two-part paper, we focus on the systematic development of graph models and the conceptual relationship between the analysis of graph models and the underlying mathematical description of the process. The elimination of spurious solutions through the use of noncausal redundant equations and thorough analysis of inverse and compensatory response is also discussed.