Using atomistic molecular dynamics (MD) simulation, we investigate the structure and energetic of single-stranded DNA (ssDNA) assisted solubilisation of single-layer graphene in aqueous medium at room temperature. We choose four different ssDNA oligonucleotides of homologous base sequences; namely, ssdA₁₂, ssdG₁₂, ssdC₁₂, ssdT₁₂ (A = Adenine, G = Guanine, C = Cytosine and T = Thymine), and one mixed base-sequence ssd(AGTC)₃, as the representative ssDNA for studying graphene dispersion in aqueous solution. We consider analysing different nucleobase binding modes and the role of several competing forces acting on ssDNA in contact with graphene in aqueous solution over the course of 30 ns MD simulation. Our simulation results show that there exist simultaneously two major competing forces: nucleobase–nucleobase intra-molecular π–π stacking interactions and nucleobase–graphene inter-molecular π–π stacking interactions. The former interactions help to maintain ssDNA helical geometry, whereas the latter interactions assist the ssDNA with becoming surface adsorbed on graphene. Note that both types of interactions strongly depend on the chemical nature of nucleobase and the sequence type present in various ssDNA. The calculated binding free energy strength between various ssDNA and graphene follows the order of: ssd(AGTC)₃ > ssdA₁₂ > ssdG₁₂ > ssdC₁₂ > ssdT₁₂. The trend in binding free energy has been rationalized in terms of the adsorption strength of individual nucleoside over graphene, number of base–graphene π-stacks, together with the nature of nucleobase (purine: A, G and pyrimidine: C, T) present in different ssDNA sequences. We find two types of ssDNA assembly on graphene; namely, coiling and elongated networks, as was also observed in recent experiment. Interestingly, the larger extent of base–graphene π-stacking interactions found for ssd(AGTC)₃ helps in forming an elongated network on graphene, and consequently, results in higher binding free energy strength. Thus, our results suggest that a mixed nucleobase sequence ssDNA, such as ssd(AGTC)₃, would be potential candidate in dispersing graphene in aqueous solution than any other homologous base sequences containing ssDNA. Additionally, we also perform the electronic structure calculations for these ssDNA–graphene composites to explore the electronic properties in details using density functional theory. We believe that our simulation results together with first-principles calculations provide great microscopic detail in understanding the ssDNA assisted dispersion of graphene in aqueous environments.