Publishing Common Neighbors Histograms of Social Networks under Edge Differential Privacy

Analyzing common neighbors between node pairs in social networks provides valuable insights into the graph structure and enables a range of network analytics tasks. In this paper, we investigate techniques to publish the histogram of common neighbor counts between all node pairs in a social network under edge-differential privacy. This problem is particularly challenging, since the histogram of common neighbor counts has a high sensitivity of O(n), where n is the number of nodes in a social network. If we inject noise into the histogram in proportion to this sensitivity to achieve edge differential privacy, then the noise would overwhelm the signals of the histogram, since each node pair can have at most n - 2 common neighbors. Existing techniques address this issue by converting the histogram publication problem to an integer partition problem that has sensitivity of O(1), but these techniques tend to yield unsatisfactory data utility as they fail to take into account the characteristics of real social networks.

To remedy the deficiency of existing methods, we propose a novel multi-stage approach that partitions the common neighbor count histogram into segments with controlled sensitivities lower than the global one, by exploiting the observation that common neighbor counts tend to follow a long-tail distribution: a small percentage of node pairs have large numbers of common neighbors while the remaining vast majority of pairs only have a few. We develop a utility-based technique to derive the optimal partition points. We conduct extensive experiments over several real social network datasets to validate our approach and evaluate the trade-offs of different design choices in our approach. Our code is available at https://github.com/VFVrPQ/edge-dp-cnh.