  As an increasing number of social networking data is published and shared for
commercial and research purposes, privacy issues about the individuals in
social networks have become serious concerns. Vertex identification, which
identifies a particular user from a network based on background knowledge such
as vertex degree, is one of the most important problems that has been
addressed. In reality, however, each individual in a social network is inclined
to be associated with not only a vertex identity but also a community identity,
which can represent the personal privacy information sensitive to the public,
such as political party affiliation. This paper first addresses the new privacy
issue, referred to as community identification, by showing that the community
identity of a victim can still be inferred even though the social network is
protected by existing anonymity schemes. For this problem, we then propose the
concept of \textit{structural diversity} to provide the anonymity of the
community identities. The $k$-Structural Diversity Anonymization ($k$-SDA) is
to ensure sufficient vertices with the same vertex degree in at least $k$
communities in a social network. We propose an Integer Programming formulation
to find optimal solutions to $k$-SDA and also devise scalable heuristics to
solve large-scale instances of $k$-SDA from different perspectives. The
performance studies on real data sets from various perspectives demonstrate the
practical utility of the proposed privacy scheme and our anonymization
approaches.
