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Vacancy defects in graphene with an odd number of missing atoms, such as the trivacancy, have been imaged at atomic resolution using aberration corrected transmission electron microscopy. These defects are not just stabilized by simple bond reconstructions between under-coordinated carbon atoms, as exhibited by even vacancies such as the divacancy. Instead we have observed reconstructions consisting of under-coordinated bridging carbon atoms spanning the vacancy to saturate edge atoms. We report detailed studies of the effect of this bridging atom on the configuration of the trivacancy and higher order odd number vacancies, as well as its role in defect stabilization in amorphous systems. Theoretical analysis using density functional theory and tight-binding molecular dynamics calculations demonstrate that the bridging atom enables the low energy reconfiguration of these defect structures.