The medical review of adverse event reports for medical products requires the processing of "big data" stored in spontaneous reporting systems, such as the US Vaccine Adverse Event Reporting System (VAERS). VAERS data are not well suited to traditional statistical analyses so we developed the FDA Adverse Event Network Analyzer (AENA) and three novel network analysis approaches to extract information from these data. Our new approaches include a weighting scheme based on co-occurring triplets in reports, a visualization layout inspired by the islands algorithm, and a network growth methodology for the detection of outliers. We explored and verified these approaches by analysing the historical signal of Intussusception (IS) after the administration of RotaShield vaccine (RV) in 1999. We believe that our study supports the use of AENA for pattern recognition in medical product safety and other clinical data.