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We propose a relationship strength estimation method in social media. We estimate relationship strength between web pages in social bookmarking services using a tag vocabulary and construct a network of the web pages. In this step Bayes theorem is used to estimate true strength from each user's strength estimation. After estimation using tags the network is represented in lower dimension space and some non-important links are removed. In this step the network is approximated keeping neighborhood of data in the original network. To evaluate our proposed method we carry out some experiments using artificially generated data and real social bookmarking data. And we confirm that 1) the proposed method can estimate more appropriate relationship strength than ordinary methods based on cooccurrence frequency and tags sharing rate and 2) the proposed method can remain essential links and delete pseudo relationship.