Tag recommendation aims to recommend to a userthe most suited tags for a given item. It is an important functionality of resource sharing systems. In this paper we propose a recommendation algorithm, called FasTag, that links the relevance of the tags to both their popularity and the opinions of the user's neighbors. FasTag assumes that the users are organized in a weighted graph representing, for instance, the similarity or the trust between them.The two salient aspects of FasTag are the scoring function it uses to evaluate the relevance of the tags, and its low computation cost. Thus, FasTag can make online recommendations, even for large datasets.Moreover, we improve the accuracy of its recommendations by adjusting automatically the size of the recommended list of tags. The experiments we did on several datasets show a significant improvement of the accuracy of the recommendations.