A rigorous classification system is foundational for biology. However, viruses offer particularly problematic classification challenges. This is because in any gram of soil or milliliter of seawater there can be many millions to billions of viruses. We can only recently “see” them (using molecular methods) and they are all busy exchanging genes between each other and with their hosts in ways that paradigms suggest should undermine any genome-based taxonomy. However, we wanted to ask the question of whether simply looking at shared genes between viruses using networks could get us on the right track towards organizing the mostly unknown and unmapped viral sequence space.