Flocking control of autonomous underwater vehicles (AUVs) has been regarded as the basis of many sophisticated marine coordination missions. However, there is still a research gap on the flocking of AUVs in weak communication and complex marine environment. This article attempts to fill up the above research gap from graph theory and intelligent learning perspectives. We first employ the bearing rigidity graph to describe the topology relationships of AUVs, through which an iterative gradient decent-based localization estimator is provided to obtain the position information. In order to improve the localization accuracy and energy efficiency, a min-weighted bearing rigidity graph generation strategy is developed. Along with this, we adopt the semi-supervised broad learning system (BLS) to design the model-free flocking controllers for AUVs in obstacle environment. The innovations of this article are summarized as follows: 1) the min-weighted bearing rigidity-based localization strategy can balance the localization accuracy and communication consumption as compared to the neighboring rule-based solutions and 2) the semi-supervised broad learning-based flocking controller can decrease the training time and solve the label limit over the supervised learning-based controllers. Finally, simulation and experimental studies are provided to verify the effectiveness.