This article leverages Wasserstein Propagation in Social Network to propose a novel distributional framework for the inference of cyber risk across interconnected economic systems. Cyber attacks represent an increasing threat to global security and economic stability, making the assessment of cyber risk particularly challenging, especially in countries with limited data availability. Using a comprehensive dataset on worldwide cyber attacks along with a set of macroeconomic indicators, we estimate risk profiles for all countries, including those with sparse information. Our approach reveals critical interdependencies and vulnerabilities among countries, highlighting the interconnected nature of cyber risks. The findings demonstrate the value of social network analysis in modelling cyber risk and the related uncertainty within cyberspace. Furthermore, the results offer actionable insights to strengthen global cybersecurity policies and improve resilience against cyber threats.