Trust systems represent a significant trend in decision support for social networks service provision. The basic idea is to allow users to rate each other even without being direct neighbors. In this case, the idea is to derive a trust score for a given user, which can assist other users in deciding whether a given node is trustful or not. We investigate the properties of trust propagation on networks, based on the notion of transitivity, and we introduce the TISoN model to generate and evaluate Trust Inference within online Social Networks. This paper highlights on these two main contributions: (i) a novel Trust Paths' Searching algorithm bwhere we define neighbors priority based on their direct trust degrees and then select trusted paths while controlling the path length; (ii) a Trust Inference Measuring algorithm TIM to build a trust network. Experimental results with data from the Advogato.com show that our work generates high quality results.