The common theme among these applications is that they emphasize many important aspects of a recommender system other than predictive accuracy: its role as an indirect way of bringing people together, its signature pattern of making connections, and the explainability of its recommendations. To address the questions raised by considering these aspects of recommendation, we propose a framework based on a mathematical model of the social network implicit in recommendation. This framework allows a more direct approach to reasoning about recommendation algorithms and their relationship to the recommendation patterns of users. We effectively ignore the issue of predictive accuracy, and so the framework is a complement to approaches based on field studies.