This paper studies learning through social networks in which agents update their beliefs by weighting those of their peers. We allow agents to pay little attention to peers with poor information at first, but more later on, as that peer acquires better information from more knowledgeable agents. We derive explicitly how social influence depends on agents' popularity (eigenvector centrality) and expertise (information precision) and show that even completely uninformed agents can contribute to social learning. In certain cases, providing better information to extremely popular agents may distract attention from the views of the experts, and lead society to worse assessments.