We propose a "layered structured network diagram," which consists of layers of time differences. We have implemented a tool called "NeL 2" for handling layered structured network diagrams. Layered structured network diagrams have multiple accumulated layers and are not single diagrams. Using this layered structure, time differences can be included in one diagram. In addition, various type of information, such as the overall tendency in a diagram during a specific period of time, can be visualized. We used layered structured network diagrams to show the co-authorship network of academic literature. Changes in the co-authorship network become visible using the layered structured network diagram. We can read various information such as changes of active research communities and other phenomena. In addition to co-authorship networks, the layered structured network diagram can be applied to the visualization of various data, such as idea processors, changes of Web sites, and others.