Visual data mining has been established to effectively analyze large, complex numerical data sets. Especially, the extraction and visualization of inherent structures such as hierarchies and networks has made a significant leap forward. However, it is still a challenging task for users to explore explicitly given large structures. In this paper, we approach this task by tightly coupling visualization and graph-theoretical methods. Therefore, we investigate if and how visualization can benefit from common graph-theoretical methods – mainly developed for the investigation of social networks – and vice versa. To accomplish this close integration, we introduce a design of a general framework for visual data mining of complex structures. Especially, this design includes an appropriate processing order of different mining and visualization algorithms and their mining results. Furthermore, we discuss some important implementation details of our framework to ensure fast structure proc...