  The increasing popularity of social networks has initiated a fertile research
area in information extraction and data mining. Anonymization of these social
graphs is important to facilitate publishing these data sets for analysis by
external entities. Prior work has concentrated mostly on node identity
anonymization and structural anonymization. But with the growing interest in
analyzing social networks as a weighted network, edge weight anonymization is
also gaining importance. We present An\'onimos, a Linear Programming based
technique for anonymization of edge weights that preserves linear properties of
graphs. Such properties form the foundation of many important graph-theoretic
algorithms such as shortest paths problem, k-nearest neighbors, minimum cost
spanning tree, and maximizing information spread. As a proof of concept, we
apply An\'onimos to the shortest paths problem and its extensions, prove the
correctness, analyze complexity, and experimentally evaluate it using real
social network data sets. Our experiments demonstrate that An\'onimos
anonymizes the weights, improves k-anonymity of the weights, and also scrambles
the relative ordering of the edges sorted by weights, thereby providing robust
and effective anonymization of the sensitive edge-weights. Additionally, we
demonstrate the composability of different models generated using An\'onimos, a
property that allows a single anonymized graph to preserve multiple linear
properties.
