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A lot of attention has been focused on peer-to-peer file sharing systems. Gnutella is a fully distributed peer-to-peer protocol without the need for a central entity. This increases the reliability of the system by avoiding a single point of failure as well making it more immune to legal attack. The two main features of the Gnutella protocol discovery of peers and searching for files are implemented by passing different types of messages between the nodes of the Gnutella overlay network. Due to its fully distributed nature, Gnutella relies on flooding to route most of these messages, which immediately raises the question of cost and scalability. We study these aspects of the Gnutella protocol by means of simulation also considering the influence of the topology of the Gnutella network.