Approximate Privacy-Preserving Neighbourhood Estimations

Anonymous social networks present a number of new and challenging problems for existing Social Network Analysis techniques. Traditionally, existing methods for analysing graph structure, such as community detection, required global knowledge of the graph structure. That implies that a centralised entity must be given access to the edge list of each node in the graph. This is impossible for anonymous social networks and other settings where privacy is valued by its participants.In addition, using their graph structure inputs for learning tasks defeats the purpose of anonymity. In this work, we hypothesise that one can re-purpose the use of the HyperANF a.k.a HyperBall algorithm -- intended for approximate diameter estimation -- to the task of privacy-preserving community detection for friend recommending systems that learn from an anonymous representation of the social network graph structure with limited privacy impact. This is possible because the core data structure maintained by HyperBall is a HyperLogLog with a counter of the number of reachable neighbours from a given node. Exchanging this data structure in future decentralised learning deployments gives away no information about the neighbours of the node and therefore does preserve the privacy of the graph structure.