In social networks, preserving privacy and preserving correlation among sensitive labels are a matter of trade-off. This paper presents a supervised anonymization technique, SNI (social network immunization), to publish social networks having multiple sensitive labels with correlation. SNI publishes all sensitive labels without distorting them. It publishes sensitive labels along with innovative labels named “partial sensitive labels” in an immune graph and multiple supplementary trees. These graph and trees, by itself or with the combination of other objects, supply correlation among sensitive labels for membership analysis. We present a framework along with an algorithm for extracting the immune graph and supplementary trees. These graph and trees minimize the membership error rate for membership analysis. The practical evaluation of the cancer code label of individuals also indicates the effectiveness of the SNI method.