In this paper, we present a description model of a Trust Network Graph (TNG)-for multi-agent-based e-commerce systems, which is similar to the relationship network formed among people's transaction activities in the real-world. The method assumes that a multi-agent system in a domain constitutes a community and so the trust network is modelled by the means of a graph in the community. Several notations and regulations are defined in the description model of TNG. In order to sweep out redundancy information in the TNG and reduce the complexity of the trust computation, we propose the principles and the processes of simplification, the definition and the selection algorithm of Optimized Path for Recommendation Propagation (OPRP) in terms of the trust commonsense in people's daily life. The examples in this paper show that TNG can describe the complex trust relationships in mutliagente-commerce systems and help simplify the algorithms of the trust evaluation.
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