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The increasing popularity of social networks has initiated a fertile researcharea in information extraction and data mining. Anonymization of these socialgraphs is important to facilitate publishing these data sets for analysis byexternal entities. Prior work has concentrated mostly on node identityanonymization and structural anonymization. But with the growing interest inanalyzing social networks as a weighted network, edge weight anonymization isalso gaining importance. We present An\'onimos, a Linear Programming basedtechnique for anonymization of edge weights that preserves linear properties ofgraphs. Such properties form the foundation of many important graph-theoreticalgorithms such as shortest paths problem, k-nearest neighbors, minimum costspanning tree, and maximizing information spread. As a proof of concept, weapply An\'onimos to the shortest paths problem and its extensions, prove thecorrectness, analyze complexity, and experimentally evaluate it using realsocial network data sets. Our experiments demonstrate that An\'onimosanonymizes the weights, improves k-anonymity of the weights, and also scramblesthe relative ordering of the edges sorted by weights, thereby providing robustand effective anonymization of the sensitive edge-weights. Additionally, wedemonstrate the composability of different models generated using An\'onimos, aproperty that allows a single anonymized graph to preserve multiple linearproperties.

Anonimos: An LP based Approach for Anonymizing Weighted Social Network Graphs