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Value Added Tax (VAT) fraud erodes public revenue and puts legitimate businesses at a disadvantaged position thereby exacerbating inequality. This article develops scalable algorithms to detect fraudulent transactions by leveraging the rich information embedded in the complex, high-dimensional VAT network structure. Supervised methods are not always suitable for VAT fraud detection, as issues in the auditing process-such as selection bias and audit quality-can seriously affect the labelling of businesses as fraudsters or not. Therefore, both supervised and unsupervised techniques in which VAT fraud detection is implemented through a suitably constructed Laplacian matrix informed by business-specific covariates. The developed methods are applied to the universe of Bulgarian VAT data and detect around 50% of the VAT fraud, outperforming well-known techniques that ignore the information provided by the transactional network structure. The proposed methods are automated and can be implemented following taxpayers' submission of their VAT returns, thus allowing the authorities to prevent large revenue losses.