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The growing need to address privacy concerns when social network data is released for mining purposes has recently led to considerable interest in various techniques for graph anonymization. In this paper, we study the following problem: Given a social network modeled as an edge-labeled graph G, we aim to make a pre-specifled subset of vertices of G k-label sequence anonymous with the minimum number of edge additions. Here, the label sequence of a vertex is the sequence of labels of edges incident to it. The contributions of this paper are two fold: We provide a framework to show hardness results for different variants of social network anonymization using a common approach. We start by showing that k-label sequence anonymity of arbitrary labeled graphs is hard, and use this result to prove NP-hardness results for many other recently proposed notions of graph anonymization. Secondly, we present interesting algorithms and hardness for bipartite graphs. For unlabeled bipartite graphs, we show k-degree anonymity is in P for all k ≥ 2. For labeled bipartite graphs, we show that k-label sequence anonymity is in P for k = 2 but it is NP-hard for k ≥ 3.