# Appropriate threshold to map a similarity value to an edge in a graph

In order to cluster users given a user-item binary matrix data, I am planning to first find user's similarity (Jaccard) and then use graph theory to isolate clusters (communities). I need to map the similarity matrix to a binary graph where $e_{ij}=1\; \text{iff}\; \text{sim}(u_i,u_j) > th$, i.e, there is an edge between nodes $i,j$ if the similarity between users $u_i$ and $u_j$ is greater than some threshold $th$.

Here is the distribution of my users' similarity:

> summary(sim)
Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.0000  0.0310  0.0910  0.1093  0.1710  0.4620

• What would be an optimum way to find an appropriate threshold?
• Is it even the right approach?
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You could retain the similarities as weights: stats.stackexchange.com/questions/2948/… – MattBagg Jan 2 '13 at 21:14
That was very helpful, thank you. – user1848018 Jan 2 '13 at 23:33