Despite effective prevention approaches, ongoing human immunodeficiency virus 1 (HIV-1) transmission remains a public health concern indicating a need for identifying its drivers. We combined a network-based clustering method using evolutionary distances between viral sequences with statistical learning approaches to investigate the dynamics of HIV transmission in the Swiss HIV Cohort Study and to predict the drivers of ongoing transmission. We found that only a minority of clusters and patients acquired links to new infections between 2007 and 2020. While the growth of clusters and the probability of individual patients acquiring new links in the transmission network was associated with epidemiological, behavioral, and virological predictors, the strength of these associations decreased substantially when adjusting for network characteristics. Thus, these network characteristics can capture major heterogeneities beyond classical epidemiological parameters. When modeling the probability of a newly diagnosed patient being linked with future infections, we found that the best predictive performance (median area under the curve receiver operating characteristic AUCROC = 0.77) was achieved by models including characteristics of the network as predictors and that models excluding them performed substantially worse (median AUCROC = 0.54). These results highlight the utility of molecular epidemiology-based network approaches for analyzing and predicting ongoing HIV transmission dynamics. This approach may serve for real-time prospective assessment of HIV transmission.