The use of persistent graph as a database repository and its incorporation in critical mission projects requires a new thinking to model the data on those graphs to follow a business logic. In this article, we present a novel approach to model a persistent graph. Our methodology for modeling is based on the ER (Entity Relationship Model). In which we introduce a set of elements to modeling a graph, such as a cardinality on the edges, type of edges, inbound/outbound edges, edges' attributes and vertex class. Our methodology for modeling serves as a specification to which the graph design must conform. Our methodology allows the designer to express models at various levels of abstraction of a graph and ensure the correctness of the logical model with respect to the conceptual model. Our Methodology enables the designer to reason about the correctness of the business logic implemented in a graph.