This paper develops a novel way for offline handwritten signature characterization using a complex networks approach in order to apply for signature verification and identification process. Complex networks can be considered among the areas of graph theory and statistical mechanics. They are suitable for shape recognition due to their properties as invariance to rotation, scale, thickness and noise. Offline signatures images were pre-processed to obtain a skeletonized version. This is represented as an adjacency matrix where there are applied degree descriptors and dynamic evolution property of complex networks in order to generate the feature vector of offline signatures. We used a database composed of 960 offline signatures groups; every group corresponds to one person with 24 genuine and 30 forged signatures. We obtained a true rate of 85.12% for identification and 76.11% for verification. With our proposal it is demonstrated that complex networks provide a promising methodology for the process of identification and verification of offline handwritten signatures and it could be used in applications like document validation.