Attributed network embedding has been widely used in modeling real-world systems. The obtained low-dimensional vector representations of nodes preserve their proximity in terms of both network topology and node attributes, upon which different analysis algorithms can be applied. Recent advances in explanation-based learning and human-in-the-loop models show that by involving experts, the performance of many learning tasks can be enhanced. It is because experts have a better cognition in the latent information such as domain knowledge, conventions, and hidden relations. It motivates us to employ experts to transform their meaningful cognition into concrete data to advance network embedding. However, learning and incorporating the expert cognition into the embedding remains a challenging task. Because expert cognition does not have a concrete form, and is difficult to be measured and laborious to obtain. Also, in a real-world network, there are various types of expert cognition such as the comprehension of word meaning and the discernment of similar nodes. It is nontrivial to identify the types that could lead to a significant improvement in the embedding. In this paper, we study a novel problem of exploring expert cognition for attributed network embedding and propose a principled framework NEEC. We formulate the process of learning expert cognition as a task of asking experts a number of concise and general queries. Guided by the exemplar theory and prototype theory in cognitive science, the queries are systematically selected and can be generalized to various real-world networks. The returned answers from the experts contain their valuable cognition. We model them as new edges and directly add into the attributed network, upon which different embedding methods can be applied towards a more informative embedding representation. Experiments on real-world datasets verify the effectiveness and efficiency of NEEC.