Unique Molecular Identifiers (UMIs) are used to distinguish identical copies of molecules from PCR amplification artifacts in high-throughput sequencing experiments. However, sequencing errors in UMIs are often overlooked or resolved informally. The authors introduce network-based methods to account for these errors when identifying PCR duplicates, improving quantification accuracy in simulated and real data sets. They demonstrate that their methods enhance reproducibility in iCLIP and single-cell RNA-seq data, and provide an open-source software package, UMI-tools, to implement these methods.Unique Molecular Identifiers (UMIs) are used to distinguish identical copies of molecules from PCR amplification artifacts in high-throughput sequencing experiments. However, sequencing errors in UMIs are often overlooked or resolved informally. The authors introduce network-based methods to account for these errors when identifying PCR duplicates, improving quantification accuracy in simulated and real data sets. They demonstrate that their methods enhance reproducibility in iCLIP and single-cell RNA-seq data, and provide an open-source software package, UMI-tools, to implement these methods.