shown to stop. According to the results of Raman, x-ray photoemission spectroscopy (XPS), $HRTEM$, and electrical transport measurements the healing takes place by annihilation of displaced carbon atoms with vacancies with assistance of thermal energy. Healing was shown to become more difficult when the size of the vacancies’ hole increases. Formation of monovacancy defects in the finite graphene flakes [@glin10] and graphene nanoribbons [@wycd12] was shown to be size-dependent, and that the vacancy defects migrate toward the edge at higher temperatures, as a result of which the structures heal themselves. DFT calculations and molecular dynamics simulations of the vacancy migration in graphene flakes show [@spb13] thermally activated motion of vacancy toward the edge occurs even at room temperature whereas the probability of return motion back to the middle is negligible.

Our [*ab-initio*]{} investigation of the vacancies and analytically study of their migration in a graphene layer supports the experimental results on magnetism measured in [@nstl12] as well as the experiments on self-healing of a graphene. Analysis of our calculation results shows that the formation energy and magnetization of divacancy is lower than those of single vacancies. Single vacancies are enough mobile, and they diffuse toward the extended defects like a 