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With the increasing popularity of Web services and Service-Oriented Architecture, we need sophisticated infrastructure to discover and compose Web services. Dynamic Web service Composition will gain wider acceptance only when the users know that the solutions obtained are comprised of trust-worthy services. In this paper, we present a framework for a Trust-based Dynamic Web service Composition that not only uses functional and non-functional attributes provided by the Web service description document but also filters and ranks solutions based on their trust rating. With the increasing popularity of Web-based Social Networks like Linkedin, Facebook, Orkut, and Twitter, there is great potential in determining the trust rating of a particular service provider or service provider organization using Social Network Analysis. We present a technique to calculate a trust rating per service using Centrality measure of Social Networks. We use this rating to further filter composition results to produce solutions that are comprised of services provided by trusted providers.