Project description: Peer-to-peer networks are decentralized computing architectures that promise to deliver scalability in data sharing and streaming applications under dynamic network conditions. In these architectures peers are connected to the network and contribute resources in return for some useful services delivered by the network. Some questions that determine the performance and robustness of the peer-to-peer network are: what is the capacity of the network? How robust is the network behavior with respect to flashcrowds and random peer failures and departures? In this project we study the performance and robustness of various peer-to-peer networks by studying various algorithms for constructing the overlay network and for determining the data packets that are transmitted . We study the properties of the complex network resulting from these algorithms in order to identify peer-to-peer networks which are both robust and efficient. Prerequisites: computer programming (C, Matlab or Python), discrete mathematics. Desired: computer networks, graph theory, probability.