The genome of bacteria is classically separated into the essential, stable and slow evolving chromosomes and the accessory, mobile and rapidly evolving plasmids. Recently, a new class of genomic elements, neither chromosomes nor plasmids, has been revealed, the nature and evolution of which proves difficult to pinpoint. In the context of characterizing the different replicons forming the bacterial genomes, we investigated the analytical methodologies best able to decipher and visualize the functional and evolutionary relationships between replicons. Using databases of genes involved in genetic information transmission systems (GITS) as inputs, we performed a global comparative genomics analysis on all available bacterial genomes according to the following methodology: i) identification and assessment of functional homologs from all bacterial genomes, ii) construction of clusters of proteins linking the bacterial replicons by their GITS, with regard to the shared functions and protein sequence homologies, iii) testing of several unsupervised approaches (visualization, clustering). The comparison of these methods relied on the biological result assessment using the replicon host taxonomy and structure as external criteria as well as stability measurements as internal criteria. Bipartite graphs proved most useful for the meaningful representation of the replicons according to their GITS proteins. Community detection algorithms (INFOMAP) performed best in terms of stability with reference to the bacterial taxonomy in comparison to traditional clustering methodologies. Furthermore, our study brought about a dual functional and taxonomical structuration of the replicon space. This led to results with strong biological implications. Indeed, we were able to characterize the third class of replicons relative to chromosomes and plasmids, and to propose novel defining criteria for these genomic elements. Beyond the biological relevance, our study sets the basis for further analyses (workflow improvement/enrichment, classifications...) in order to bring to light driving forces of genome evolution.