Social networks facilitate information sharing and communication among people who have common interests. Although social networks have been widely used to compute the reputations of Web services, they are limited in the ability to support the sophisticated estimation of service reputations. This paper proposes a sophisticated method of computing service reputations, which considers service requesters, raters and providers participating in the service ecosystem. In order to represent the interactions among the service participants, we also propose an integrated model which combines social and service network models. Based on the model, the proposed method calculates the credibility and expertise of the raters and providers of a service and applies them to the reputation of the service. Experimental results with real-world Web services show that the proposed method computes service reputations elaborately.