The invention provides systems and methods for analyzing viruses by representing viral genetic diversity with a directed acyclic graph (DAG), which allows genetic sequencing technology to detect rare variations and represent otherwise difficult-to-document diversity within a sample. Additionally, a host-specific sequence DAG can be used to effectively segregate viral nucleic acid sequence reads from host sequence reads when a sample from a host is subject to sequencing. Known viral genomes can be represented using a viral reference DAG and the viral sequence reads from the sample can be compared to viral DAG to identify viral species or strains from which the reads were derived. Where the viral sequence reads indicate great genetic diversity in the virus that was infecting the host, those reads can be assembled into a DAG that itself properly represents that diversity.