Identifying Similar Neighborhood Structures in Private Social Networks

Many social networks being analyzed today are generated from sources with privacy concerns. A number of network centrality measures have been introduced to better quantify various social dynamics of interest to social scientists. In this paper, we propose an approximation of a social network that allows for certain centrality measures to be calculated while hiding information about the full network. Our approximation is not a perturbed graph, but rather a generalize trie structure containing a network hop expansion set for each node in the graph. We show that a network with certain topological structures, naturally hides nodes and increases the number of candidate nodes in each equivalence class. The storage of our graph approximation naturally clusters nodes of the network with similar graph expansion structure and therefore, can also be used as the basis for identifying ´like´ nodes in terms of similar structural position in the network. For branches of the trie that are not private enough, we introduce heuristics that locally merges segments of the trie to enforce k-node anonymity.