An ideal network window electrode for photovoltaic applications should provide an optimal surface coverage, a uniform current density into and/or from a substrate, and a minimum of the overall resistance for a given shading ratio. Here we show that metallic networks with quasi-fractal structure provides a near-perfect practical realization of such an ideal electrode. We find that a leaf venation network, which possesses key characteristics of the optimal structure, indeed outperforms other networks. We further show that elements of hierarchal topology, rather than details of the branching geometry, are of primary importance in optimizing the networks, and demonstrate this experimentally on five model artificial hierarchical networks of varied levels of complexity. In addition to these structural effects, networks containing nanowires are shown to acquire transparency exceeding the geometric constraint due to the plasmonic refraction.