In the software rich environment of 6G, systems will be surrounded by edge devices that support distributed software systems which are critical to operations. Such systems may also be subject to frequent updates or uploads of individual software components. Trust in such systems will therefore depend on our ability to rapidly ensure that such software is not vulnerable to cyberattacks or malicious compromises. Thus this paper presents a novel System-Wide Vulnerability Assessment (SWVA) framework based on Machine Learning, that can be frequently activated to assess the vulnerability of interconnected software components over edge systems. The performance of the SWVA framework is illustrated by assessing the vulnerability of 13 versions of a real world 11 component software system, and comparingthe ARNN results against the well-known ML models MLP, KNN, and Lasso. The results show the superior performance of SWVA, offering over 85% median accuracy and good scalability as the number of connected software components increases.