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Nanoporous metallic materials are of great interest to the scientific and industrial communities. To better tailor the mechanical properties to the functional needs, here we examined open-cell nanocrystalline tungsten nanofoams to provide fundamental insight into the correlations between cellular structures and mechanical properties. Depth-sensing nanoindentation tests were performed on tungsten nanofoams with independently varied relative densities and cellular structures to obtain foam mechanical properties. For tungsten nanofoams with self-similar and highly ordered cellular structures, the Young's modulus is insensitive to the ligament size, but varies with the relative density in a close way to the classical Gibson-Ashby scaling law. The flow strength of these regular nanofoams follows the classical scaling behavior only when properly taking into consideration the ligament size effect and corrections for the relative density. Contrarily, tungsten nanofoams with a certain relative density but varied cellular structures exhibit deterioration of both, Young's modulus and flow strength, with increasing structural disorders. This study emphasizes the importance of structural self-similarity when applying the established scaling laws to describe the foam mechanical properties. Meanwhile, it demonstrates that for optimized performance of the nanofoams, cellular architecture is the key factor of consideration.