  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.
