The genome of the influenza virus consists of eight distinct single-stranded RNA segments, each encoding proteins essential for the viral life cycle. When the virus infects a host cell these segments must be replicated and packaged into new budding virions. The viral genome is assembled with remarkably high fidelity: experiments reveal that most virions contain precisely one copy of each of the eight RNA segments. Cellbiological studies suggest that genome assembly is mediated by specific reversible and irreversible interactions between the RNA segments and their associated proteins. However, the precise inter-segment interaction network remains unresolved. Here we computationally predict that tree-like irreversible interaction networks guarantee high-fidelity genome assembly, while cyclic interaction networks lead to futile or frustrated off-pathway products. We test our prediction against multiple experimental datasets. We find that tree-like networks capture the nearestneighbor statistics of RNA segments in packaged virions, as observed by EM tomography. Just eight tree-like networks (of a possible 262,144) optimally capture both the nearest-neighbor data as well as independently measured RNA-RNA contact propensities. These eight do not include the previously-proposed hub-and-spoke and linear networks. Rather, each predicted network combines hub-like and linear features, consistent with evolutionary models of interaction gain and loss.Segmented virus | Influenza |Self-assembly | Network evolution