Graphene is a promising candidate as a two-dimensional support material for catalysis. However, more research is still needed on the catalytic properties of this material from a theoretical perspective. Factors such as defects and doping can significantly influence the structural, chemical, electrical, and magnetic properties of graphene. The physical properties of a single atom or a dimer of Fe, Co, and Ni covalently bonded to the four pyridinic nitrogen atoms substituted in graphene is an exciting topic. In this study, we used VASP to explore the electronic structure of the defective graphene systems. For various dopant models with a single metal atom and the dimer, we calculated the densities of states to study the electronic structure and magnetism of these systems. Our computational results showed that a single Fe atom and a Fe-Fe dimer are promising for doping. In the heterogeneous dimer structures, we found that the spin magnetic moments of the metal atoms may disappear or decrease, depending on which two atoms are paired. In future, we will study the molecular adsorption properties on these systems.