Attributed networks are pervasive in numerous of high-impact domains. As opposed to conventional plain networks where only pairwise node dependencies are observed, both the network topology and node attribute information are readily available on attributed networks. More often than not, the nodal attributes are depicted in a high-dimensional feature space and are therefore notoriously difficult to tackle due to the curse of dimensionality. Additionally, features that are irrelevant to the network structure could hinder the discovery of actionable patterns from attributed networks. Hence, it is important to leverage feature selection to find a high-quality feature subset that is tightly correlated to the network structure. Few of the existing efforts either model the network structure at a macro-level by community analysis or directly make use of the binary relations. Consequently, they fail to exploit the finer-grained tie strength information for feature selection and may lead to suboptimal results. Motivated by the sociology findings, in this work, we investigate how to harness the tie strength information embedded on the network structure to facilitate the selection of relevant nodal attributes. Methodologically, we propose a principled unsupervised feature selection framework ADAPT to find informative features that can be used to regenerate the observed links and further characterize the adaptive neighborhood structure of the network. Meanwhile, an effective optimization algorithm for the proposed ADAPT framework is also presented. Extensive experimental studies on various real-world attributed networks validate the superiority of the proposed ADAPT framework.