  Complex networks usually expose community structure with groups of nodes
sharing many links with the other nodes in the same group and relatively few
with the nodes of the rest. This feature captures valuable information about
the organization and even the evolution of the network. Over the last decade, a
great number of algorithms for community detection have been proposed to deal
with the increasingly complex networks. However, the problem of doing this in a
private manner is rarely considered. In this paper, we solve this problem under
differential privacy, a prominent privacy concept for releasing private data.
We analyze the major challenges behind the problem and propose several schemes
to tackle them from two perspectives: input perturbation and algorithm
perturbation. We choose Louvain method as the back-end community detection for
input perturbation schemes and propose the method LouvainDP which runs Louvain
algorithm on a noisy super-graph. For algorithm perturbation, we design
ModDivisive using exponential mechanism with the modularity as the score. We
have thoroughly evaluated our techniques on real graphs of different sizes and
verified their outperformance over the state-of-the-art.
