HIV-1 reservoirs display heterogeneous nature, lodging both intact and defective proviruses. Recent evidence has shed light on their difference, particularly in the context of immune-mediated selection. To deepen our understanding of such heterogeneous HIV-1 reservoirs and their functional implications, we pioneered the integration of basic concepts of graph theory to characterize the composition of HIV-1 reservoirs. Our analysis revealed noticeable topological properties in networks, featuring immunologic signatures enriched by genes harboring intact and defective proviruses, when comparing antiretroviral therapy (ART)-treated HIV-1-infected individuals and elite controllers. The key variable, the rich factor, played a pivotal role in classifying distinct topological properties in networks. The host gene expression strengthened the accuracy of classification between elite controllers and ART-treated patients. Overall, our work provides a prime example of leveraging genomic approaches alongside mathematical tools to unravel the complexities of HIV-1 reservoirs.