Computing in social networks with relationship algebra

Communities are the latest phenomena on the Internet. At the heart of each community lies a social network. In this paper, we show a generalized framework to understand and reason in social networks. Previously, researchers have attempted to use inference-specific type of relationships. In this paper, we propose a framework to represent and reason with general case of social relationship network in a formal way. We call it relationship algebra. In this paper, we first present this algebra then show how this algebra can be used for various interesting computing on a social network weaved in the virtual communities. We show applications such as determining reviewers in a semi-professional network maintained by conference management systems, finding conflict of interest in a publication system, or to infer various trust relationships in a community of close associates etc. We also show how future community networks can be used to determine who should be immunized in the case of a contagious disease outbreak and how these networks could be used in crime prevention etc.