Large amounts of data generated everyday by different organizations for various purposes have catalyzed research opportunities related to data science. Publishing raw data may raise security concerns among the users or actors who have provided some sensitive information in the raw data. Over the years, it has been observed that attackers can very easily exploit the sensitive information as well as the identity of the users from the raw data. Thus, to protect the identity of the users in the anonymized data, the notion of k-anonymity and its improved version l-diversity have been proposed. Several algorithms have been developed to achieve k-anonymity as well as l-diversity for both relational micro-data and social network data. In this paper, we propose an approach based on the eigenvector centrality value of the individual nodes to achieve k-anonymity as well as l-diversity by adding noise nodes in the raw data. In the process of adding noise nodes, we focused on adding noise nodes in such an intelligent manner so that they have very little influence on the anonymized data. Our proposed algorithm also ensures minimal changes in the social influence of the nodes in the anonymized data which are already present in the raw data. Through various measures and experiments, we establish the effectiveness of our proposed algorithm over the several existing social network anonymization techniques. © 2016 - IOS Press and the authors. All rights reserved.