This research develops a novel system science approach to examine the potential risk of outbreaks caused by geographical clustering of underimmunized individuals for an infectious disease like measles. We use an activity-based population network model and school immunization records to identify underimmunized clusters of zip codes in the Commonwealth of Virginia. Although Virginia has high vaccine coverage for measles at the state level, finer-scale investigation at the zip code level finds three statistically significant underimmunized clusters. This research examines why some underimmunized geographical clusters are more critical in causing outbreaks and how their criticality changes with a possible drop in overall vaccination coverage. Results show that different clusters can cause vastly different outbreaks in a region, depending on their size, location, immunization rate and network characteristics. Among the three underimmunized clusters, we find one to be critical and the other two to be benign in terms of an outbreak risk. However, when the vaccine coverage among children drops by just 5% (or 0.8% overall in the population), one of the benign clusters becomes highly critical. This work also examines the demographic and network properties of these clusters to identify factors that are responsible for affecting the criticality of the clusters. Although this work focuses on measles, the methodology is generic and can be applied to study other infectious diseases.