Assembling DNA fragments based on their overlaps remains the main assembly paradigm with long DNA fragments sequencing technologies, independently of the aim to resolve only one or several haplotypes. Since an overlap can be seen as a succession relationship between two oriented fragments, the directed graph structure has emerged as an appropriate data structure for handling overlaps. However, this graph paradigm does not appear to take benefit of the reverse symmetry of the orientated fragments and their overlaps, which is a result of blind DNA double-strand sequencing. Thus, the bi-directed graph paradigm was introduced in 1995 towards reducing the graph size by handling the reverse symmetry, and becomes since then the main graph paradigm used in assembly/scaffolding methods. Nevertheless, the available graph paradigms have never been contrasted before, and no implementations have been described. Here we make a complete review on the existing overlap graph paradigms. Furthermore, we present suitable data structures that are theoretically compared in terms of time and memory consumption in the context of the design of some basic graph algorithms. We also show that each one of the paradigms can be switched to another by slightly modifying their data structures.