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In this work, we perform a numerical study on artificial spin ice systems formed by square arrays of ferromagnetic nano-islands. Inspired by topological studies, we consider absent nano-islands at random positions throughout the array. The system is described by a Hamiltonian that includes anisotropy energy as well as dipolar interaction among the islands in the Heisenberg spin model approach. The simulations were done in the framework of the Monte-Carlo method with the Metropolis algorithm. We focus on the effect of the vacancies on the magnetic vertices configurations. In particular, we calculate the distribution of all possible magnetic configurations of the vertices as a function of the percentage of vacancies. The absent nano-islands generate a loss of geometric frustration, and the system evolves faster than the system without vacancies to a lower energy state. However, the system shows the difficulty of …