Fibrin networks, formed during blood clotting, have a large and complicated structure and play a crucial role in regulating blood clot growth. Identifying and analyzing the 3D topological structure of fibrin networks using fluorescence confocal microscopy images is challenging due to their complex anatomy, and known automated methods do not seem to work well. In this paper, we present a two-stage approach for identifying the topological structure of fibrin networks in 3D confocal microscopy images. The first stage segments fibrin networks using a new Indicator-Guided Adaptive Thresholding (IGAT) algorithm. The second stage extracts, prunes, and analyzes the skeleton of fibrin networks in order to identify their topological structure. A new approach based on orientation analysis is applied to refine the extracted topological structure. Evaluation on 3D confocal microscopy images demonstrates that our approach is not sensitive to parameter selection and outperforms the known method, reducing the false positive rate for detecting branch points by 24% and reducing the false negative rate for detecting fiber segments by 15%.