Since the first uptake of electric vehicles, policy makers are questioning how to rollout public charging infrastructure in an efficient manner, such that user convenience balances with costs of investment. In some metropolitan areas, the first phase of rollout has been passed, meaning an optimized deployment of future charging stations for electric vehicles (EVs) becomes important to improve the charging infrastructure and ensure customer satisfaction and sufficient service provision. Complex system literature shows that network vulnerability is an important metric, yet, charging infrastructure has not yet been a subject of these simulation models so far. This research, based on real-world data, provides a novel approach for improving the roll-out strategy of municipalities, by treating the charge infrastructure as a complex network of charging stations and defining vulnerability in respect to the availability of its surrounding charging stations within relevant walking distance.