The COVID-19 pandemic brought not only global devastation but also an unprecedented infodemic of false or misleading information that spread rapidly through online social networks. Network analysis plays a crucial role in the science of fact-checking by modeling and learning the risk of infodemics through statistical processes and computation on mega-sized graphs. This article proposes MEGA, Machine Learning-Enhanced Graph Analytics, a framework that combines feature engineering and graph neural networks to enhance the efficiency of learning performance involving massive graphs. Infodemic risk analysis is a unique application of the MEGA framework, which involves detecting spambots by counting triangle motifs and identifying influential spreaders by computing the distance centrality. The MEGA framework is evaluated using the COVID-19 pandemic Twitter dataset, demonstrating superior computational efficiency and classification accuracy.