Node-link diagrams are widely used to visualize the relational structure of real world datasets. As identical data can be visualized in infinite ways by simply changing the spatial arrangement of the nodes, one of the important research topics of the graph drawing community is to visualize the data in the way that can facilitate people's comprehension. The last three decades have witnessed the growth of algorithms for automatic visualization. However, despite the popularity of node-link diagrams and the enthusiasm in improving computational efficiency, little is known about how people read these graphs and what factors (layout, size, density, etc.) have impact on their effectiveness (the usability aspect of the graph, e.g., are they easy to understand?). This thesis is comprehensive research to investigate the factors that affect people's understanding of node-link diagrams using eye-tracking methods. Three experiments were conducted, including 1) a pilot study with 22 participants to explore the layout and size effect; 2) an eye tracking experiment with 43 participants to investigate the layout, size and density effect on people's graph comprehension using abstract node-link diagram and generic tasks; and 3) an eye tracking experiment with the same participants to investigate the same effects using a real visualization analytic application. Results showed that participants' spatial reasoning ability had significant impact on people's graph reading performance. Layout, size, and density were all found to be significant effects under different task circumstances. The applicability of the eye tracking methods on visualization evaluation has been confirmed by providing detailed evidence that demonstrates the cognitive process of participants' graph reading behavior.