Freshwater species populations remain at the forefront of global biodiversity loss. Incomplete knowledge on large scale biodiversity patterns challenges robust conservation measures to counteract this trend. The underlying dendritic network structure of freshwater systems greatly impacts the spatial distribution of freshwater biodiversity. Despite its importance, the integration of network properties such as centrality indices and connectivity into freshwater biodiversity analyses and predictive models still consists of a slow process and is lacking in large-scale analyses. With its heterogeneous freshwater habitats, South America harbors one of the most diverse ichthyofauna in the world. South American freshwater fish hence represents an ideal case study to investigate (i) how freshwater habitats are structured and connected within the hydrographic network across large spatial gradients and at high spatial resolution and (ii) what role the network structure and connectivity play in regard to complementary diversity patterns. In this study, we employ graph theory to abstract the stream and lake network from the high resolution Hydrography90m dataset across South America and compute a suite of connectivity indices, e.g., identifying irreplaceable parts central to maintaining connectivity. These indices are then integrated in graph-based species distribution models, linking them with freshwater fish occurrence records and morphological traits, to map species richness, range size patterns and functional diversity distributions. Capitalizing on the large-scale network analyses at high spatial resolution allows to provide vital information for area-based conservation targets and to address the non-trivial question towards the decision where to prioritize freshwater conservation efforts.