This paper presents (Elementary) Mathematical Data Models of the Relational and the Entity-Relationship Data Models. The first one was obtained starting with a Relational Data Model of itself shown in our Conceptual Data Modeling and Database Design book (Volume 1: The Shortest Advisable Path) and then applying several forward and reverse engineering algorithms between these two data models, as well as the Entity-Relationship one. The second one was obtained directly from the Entity-Relationship Data Model of itself also shown in our book.
Keywords: Conceptual Data Modeling; Relational Data Model; Entity-Relationship Data Model; E-R diagram cycle analysis; (Elementary) Mathematical Data Model; Relational and Entity-Relationship Database Management Systems design