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Aluminoborate glasses find use as sealants in numerous energy-storage and biomedical devices. However, a primary shortcoming of this glass family is its chemical durability, particularly when they may be exposed to alkaline (aqueous) environments. The structural features of such glasses, namely the network-modifying elements are thought to regulate such durability, e.g., due to the changes they induce in the coordination of network-forming elements. Herein, by systematic analyses of dissolution rates – a proxy for chemical durability – of a wide range of aluminoborate glasses containing network modifiers of diverse field strengths, it is shown that network modifiers affect the atomic topology of the glass network in relation to field strength. This reveals a general scaling of aluminoborate glass dissolution rates as a function of their atomic network's rigidity. The outcomes highlight pathways that could be used to improve the chemical durability of aluminoborate glasses by compositional alterations (i.e., selecting network modifiers) that enhance network rigidity.