Current peer-to-peer systems are targeted for information sharing, file storage, searching and indexing often using an overlay network. In this paper we expand the scope of peer-to-peer systems to include the concept of "communities". Communities are like interest groups, modeled after human communities and can overlap. They can also exist without anyone knowing about their existence. Communities are created, implicitly when one or more entities claim an interest in the same topic. Our work focuses on efficient methods to discover the formation of these self-configuring communities. We investigate the behavior of randomly created communities and model the complexity of discovery algorithms. Discovering communities on the fly is essential to being able to perform community directed searching. In addition, efficient discovery algorithms allow us to manage quickly changing community structures (dynamic communities, failures, mobile nodes and so on). We use some simulations to discover the architecture of randomly created communities and then perform studies on techniques for discovering communities.
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