Abstract Public health genomic surveillance systems typically measure genome relatedness and infer molecular epidemiological relationships using chromosomal loci alone – an approximation of vertical evolution, or homology-by-descent. The accessory genome, composed of plasmids and other mobile genetic elements, reflects horizontal gene transfer and serves as an important mechanism of bacterial evolution, enabling rapid adaptation. Measuring homology in the accessory genome – homology-by-admixture – could offer important molecular epidemiological information for public health application. We applied Jaccard Index and a novel genome length distance metric to compute pangenome relatedness for the globally-important pathogen Salmonella enterica serotype Typhi (Typhi), and graphically express both homology-by-descent and homology-by-admixture in a reticulate network. Jaccard Index Network Analysis revealed structure in the Typhi pangenome that can be harnessed to enhance discriminatory power for surveillance, track antimicrobial resistance, and refine our understanding of homology for outbreak management and prevention. This offers a more intricate, multidimensional framework for understanding pathogen evolution. Significance Statement Bacterial relatedness is often measured and visualized using chromosomal comparison and phylogenetic trees. While valuable, this approach captures only the vertical evolutionary dimension and excludes genetic material acquired or lost through horizontal gene transfer. We present an approach for measuring and visualizing bacterial relatedness using all core and accessory genetic material and discuss the interpretation of resulting reticulate networks of bacterial genomes. In application to Salmonella Typhi, Jaccard Index Network Analysis revealed structure in populations of this pathogen that may be harnessed for public health applications. This approach captures both vertical and horizontal evolutionary dimensions, offering an intricate genetic framework for exploring pathogen evolution.