Artificial graphene is an artificial honeycomb structure which mimics the interesting properties of graphene. Such as Dirac cone in energy dispersion, zero band gap etc. Wide range of production type makes artificial graphene valuable material. It can be engineered by lasers, molecules, and semiconductors. Semiconductor based artificial graphene can be produced by dot lattice with honeycomb patterned attractive potential or by antidot lattice with triangular patterned repulsive potential. In the following calculations, semiconductor (GaAs) based artificial graphene was used to compute electronic properties. Like in graphene, artificial graphene has Dirac cones in energy dispersion. However, graphene has 1.42 °A carbon to carbon atom distance. This distance can not be changed but artificial graphene offers us tunability. Different parameters yield tons of band structure. It offers not only Dirac cone but also gaped bands in energy dispersion. This graphene-like feature and tunability make artificial graphene an important and researchable subject. Besides, we added another tunable parameter stiffness to control the shape of potential. Stiffness became another important parameter in our calculations. We observed that stiffness dramatically changes the band structure of the material. As a first step, artificial graphene band structures are calculated from the singleelectron approximation. Some parameters are compared with other works and the same results are found. Dirac cones are achieved in band structures. Hopping and Hubbard U values are computed. Those parameters are essential for computing finite structures. Mean-field Hubbard can be solved, and wave functions can be used as input for input required methods such as quantum Monte Carlo. As a second step, we used the density functional theory method to investigate electron-electron interactions. Local density approximation was chosen to solve the Kohn- Sham equation. Hopping parameters obtained from DFT are much realistic than the single-electron approximation. Stiffness plays a big role in DFT energy dispersion. Different stiffness values result in different band structures. Those stiffness values influence Dirac cones and their slope. So that stiffness changes the hopping parameter.