HIV-1 reservoirs display a heterogeneous nature, lodging both intact and defective proviruses. To deepen our understanding of such heterogeneous HIV-1 reservoirs and their functional implications, we integrated 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. Markov chain modeling for the simulation of different graph networks demonstrated the presence of an intrinsic barrier between elite controllers and non-elite controllers. Overall, our work provides a prime example of leveraging genomic approaches alongside mathematical tools to unravel the complexities of HIV-1 reservoirs.