Data privacy for simply anonymized network logs represented as graphs - considerations for graph alteration operations.

In this paper we review the state of the art on graph privacy with special emphasis on applications to online social networks, and we consider some novel aspects which have not been greatly covered in the specialized literature on graph privacy. The following key considerations are covered: (i) choice of different operators to modify the graph; (ii) information loss based on the cost of graph operations in terms of statistical characteristics (degree, clustering coefficient and path length) in the original graph; (iii) computational cost of the operations; (iv) in the case of the aggregation of two nodes, the choice of similar adjacent nodes rather than isomorphic topologies, in order to maintain the overall structure of the graph; (v) a statistically knowledgeable attacker who is able to search for regions of a simply anonymized graph based on statistical characteristics and map those onto a given node and its immediate neighborhood.This research is partially supported by the Spanish MEC (projects ARES CONSOLIDER INGENIO 2010 CSD2007-00004--eAEGIS TSI2007-65406-C03-02).Peer Reviewe