DNA flows between chromosomes and mobile elements, following rules that are poorly understood. This limited knowledge is partly explained by the limits of current approaches to study the structure and evolution of genetic diversity. Network analyses of 119,381 homologous DNA families, sampled from 111 cellular genomes and from 165,529 phage, plasmid, and environmental virome sequences, offer challenging insights. Our results support a disconnected yet highly structured network of genetic diversity, revealing the existence of multiple "genetic worlds." These divides define multiple isolated groups of DNA vehicles drawing on distinct gene pools. Mathematical studies of the centralities of these worlds' subnetworks demonstrate that plasmids, not viruses, were key vectors of genetic exchange between bacterial chromosomes, both recently and in the past. Furthermore, network methodology introduces new ways of quantifying current sampling of genetic diversity.evolution | lateral gene transfer | mobile genetic elements | phages | plasmids