Run time variability of parallel application codes continues to be a significant challenge in clusters. We are studying run time variability at the communication level from the perspective of the application, focusing on the network. To gain insight into this problem our earlier work developed a tool to emulate parallel applications and in particular their communication. This framework, called Parallel Application Communication Emulation (PACE) has produced interesting insights regarding network performance in NOW clusters. A Parallel Application Run Time Sensitivity Evaluation (PARSE) function has been recently added to the PACE framework to study the run time effects of controlled network performance degradation. This work introduces PARSE and presents experimental results from tests conducted on several widely used parallel benchmarks and application code fragments. The results suggest that parallel applications can be classified in terms of their sensitivity to network performance variation.