Anonymizing Weighted Social Network Graphs

The increasing popularity of social networks has initiated a fertile research area in information extraction and data mining. Although such analysis can facilitate better understanding of sociological, behavioral, and other interesting phenomena, there is a growing concern about personal privacy being breached, thereby requiring effective anonymization techniques. In this paper, we consider edge weight anonymization in social graphs. Our approach builds a linear programming (LP) model which preserves properties of the graph that are expressible as linear functions of the edge weights. Such properties form the foundations of many important graph-theoretic algorithms such as shortest paths, k-nearest neighbors, minimum spanning tree, etc. Off-the-shelf LP solvers can then be used to find solutions to the resulting model where the computed solution constitutes the weights in the anonymized graph. As a proof of concept, we choose the shortest paths problem, and experimentally evaluate the proposed techniques using real social network data sets.