Much of the visual analysis of a graph reduces to a set of building-block visual tasks such as node scanning or edge and path tracing. These tasks may be trivial in small graphs but increase in complexity the larger and denser a graph visualization becomes. In this work, we use eye-tracking data as a real-time input to alter a graph visualization interactively and support its analysis. Specifically, we display labels of fixated nodes, we highlight edges as they are visually traced, and we dim out edges that pass through a users view-focus while having their endpoints far outside of it. We conducted a small informal user study to compare the performance of our eye-tracking enabled graph visualization versus a graph visualization system that only uses mouse input. The gaze-enabled visualization performed better in terms of accuracy and response time and was preferred by all participants.