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High-performance solution-processed organic semiconductors maintain macroscopic functionality even in the presence of microscopic disorder. Here we show that the functional robustness of certain organic materials arises from the ability of molecules to create connected mesoscopic electrical networks, even in the absence of periodic order. The hierarchical network structures of two families of important organic photovoltaic acceptors, functionalized fullerenes and perylene diimides, are analyzed using a newly developed graph methodology. The results establish a connection between network robustness and molecular topology, and also demonstrate that solubilizing moieties play a large role in disrupting the molecular networks responsible for charge transport. A clear link is established between the success of mono and bis functionalized fullerene acceptors in organic photovoltaics and their ability to construct mesoscopically connected electrical networks over length scales of 10 nm. [ABSTRACT FROM AUTHOR]