Peer-to-peer networks are envisioned to be deployed for a wide range of applications. However, P2P networks evolving in an unorganized manner suffer from serious scalability problems, limiting the number of nodes in the network, creating network overload and pushing search times to unacceptable limits. We address these problems by imposing a deterministic shape on P2P networks: We propose a graph topology which allows for very efficient broadcast and search, and we describe a broadcast algorithm that exploits the topology to reach all nodes in the network with the minimum number of messages possible. We provide an efficient topology construction and maintenance algorithm which, crucial to symmetric peer-to-peer networks, does neither require a central server nor super nodes in the network. Nodes can join and leave the self-organizing network at any time, and the network is resilient against failure. Moreover, we show how our scheme can be made even more efficient by using a global ontology to determine the organization of peers in the graph topology, allowing for efficient concept-based search.