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Service providers of social network based services release their sanitized graph structure for third parties (e.g., business partners) from time to time. However, as these releases contain valuable information additionally to what is publicly available in the network, these may be targeted by re-identification attacks, i.e., where an attacker tries to recover the identities of the nodes that were removed during the sanitization process. One powerful type of these, called structural re-identification attacks consider only structural properties, and work according to a specific strategy: first they re-identify some nodes by their globally unique properties, and then in an optional second phase, nodes related to these are re-identified by their locally unique properties. Global re-identifiability or global node anonymity is a well studied concept, however, node anonymity for local re-identification has not yet been analyzed. Therefore in this paper, after discussing the related literature on anonymity and re-identification, we introduce the novel term of Local Topological Anonymity (LTA), which describes the resistant power of a node against local re-identification attacks, or, in other words, indicates how well the node is structurally hidden in her neighborhood. Regarding these attacks in the literature, we propose three measure variants of LTA based on structural similarity measures, and evaluate them by visual inspection and simulation in multiple networks. We show that one of the proposed measures provides good prediction on local node re-identifiability as there is correlation between the LTA values and the re-identification statistics provided by the state-of-the-art algorithm.