The confluence of electron correlations and spin-orbit interactions is critical to realizing quantum phases in 5d transition metal oxides. Here, we investigate how the strength of the effective electron correlations evolve across a series of d5 iridates comprised of IrO6 octahedra, ranging from the layered correlated insulator Sr2IrO4, to the three-dimensional perovskite semimetal SrIrO3, to metallic rutile IrO2 in which the octahedra are arranged in a mixed edge and corner sharing network. Through a combination of reactive oxide molecular-beam epitaxy, in situ angle-resolved photoemission spectroscopy, core level photoemission, and density functional theory, we show how the effective electron correlations weaken as a function of increasing connectivity of the IrO6 network and p-d hybridization. Our results demonstrate how structure and connectivity can be used to control the strength of correlations in the iridates. © 2016 American Physical Society.